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Simplifying (2 + -1x)(x + -2) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Reorder the terms: (2 + -1x)(-2 + x) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Multiply (2 + -1x) * (-2 + x) (2(-2 + x) + -1x * (-2 + x)) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) ((-2 * 2 + x * 2) + -1x * (-2 + x)) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) ((-4 + 2x) + -1x * (-2 + x)) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) (-4 + 2x + (-2 * -1x + x * -1x)) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) (-4 + 2x + (2x + -1x2)) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Combine like terms: 2x + 2x = 4x (-4 + 4x + -1x2) + -1(2 + -1x)(x + 2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Reorder the terms: -4 + 4x + -1x2 + -1(2 + -1x)(2 + x) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Multiply (2 + -1x) * (2 + x) -4 + 4x + -1x2 + -1(2(2 + x) + -1x * (2 + x)) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -4 + 4x + -1x2 + -1((2 * 2 + x * 2) + -1x * (2 + x)) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -4 + 4x + -1x2 + -1((4 + 2x) + -1x * (2 + x)) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -4 + 4x + -1x2 + -1(4 + 2x + (2 * -1x + x * -1x)) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -4 + 4x + -1x2 + -1(4 + 2x + (-2x + -1x2)) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Combine like terms: 2x + -2x = 0 -4 + 4x + -1x2 + -1(4 + 0 + -1x2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -4 + 4x + -1x2 + -1(4 + -1x2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -4 + 4x + -1x2 + (4 * -1 + -1x2 * -1) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -4 + 4x + -1x2 + (-4 + 1x2) = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Reorder the terms: -4 + -4 + 4x + -1x2 + 1x2 = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Combine like terms: -4 + -4 = -8 -8 + 4x + -1x2 + 1x2 = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Combine like terms: -1x2 + 1x2 = 0 -8 + 4x + 0 = (x + -6)(x + 1) + -1(5x + -1x2 + 10) -8 + 4x = (x + -6)(x + 1) + -1(5x + -1x2 + 10) Reorder the terms: -8 + 4x = (-6 + x)(x + 1) + -1(5x + -1x2 + 10) Reorder the terms: -8 + 4x = (-6 + x)(1 + x) + -1(5x + -1x2 + 10) Multiply (-6 + x) * (1 + x) -8 + 4x = (-6(1 + x) + x(1 + x)) + -1(5x + -1x2 + 10) -8 + 4x = ((1 * -6 + x * -6) + x(1 + x)) + -1(5x + -1x2 + 10) -8 + 4x = ((-6 + -6x) + x(1 + x)) + -1(5x + -1x2 + 10) -8 + 4x = (-6 + -6x + (1 * x + x * x)) + -1(5x + -1x2 + 10) -8 + 4x = (-6 + -6x + (1x + x2)) + -1(5x + -1x2 + 10) Combine like terms: -6x + 1x = -5x -8 + 4x = (-6 + -5x + x2) + -1(5x + -1x2 + 10) Reorder the terms: -8 + 4x = -6 + -5x + x2 + -1(10 + 5x + -1x2) -8 + 4x = -6 + -5x + x2 + (10 * -1 + 5x * -1 + -1x2 * -1) -8 + 4x = -6 + -5x + x2 + (-10 + -5x + 1x2) Reorder the terms: -8 + 4x = -6 + -10 + -5x + -5x + x2 + 1x2 Combine like terms: -6 + -10 = -16 -8 + 4x = -16 + -5x + -5x + x2 + 1x2 Combine like terms: -5x + -5x = -10x -8 + 4x = -16 + -10x + x2 + 1x2 Combine like terms: x2 + 1x2 = 2x2 -8 + 4x = -16 + -10x + 2x2 Solving -8 + 4x = -16 + -10x + 2x2 Solving for variable 'x'. Reorder the terms: -8 + 16 + 4x + 10x + -2x2 = -16 + -10x + 2x2 + 16 + 10x + -2x2 Combine like terms: -8 + 16 = 8 8 + 4x + 10x + -2x2 = -16 + -10x + 2x2 + 16 + 10x + -2x2 Combine like terms: 4x + 10x = 14x 8 + 14x + -2x2 = -16 + -10x + 2x2 + 16 + 10x + -2x2 Reorder the terms: 8 + 14x + -2x2 = -16 + 16 + -10x + 10x + 2x2 + -2x2 Combine like terms: -16 + 16 = 0 8 + 14x + -2x2 = 0 + -10x + 10x + 2x2 + -2x2 8 + 14x + -2x2 = -10x + 10x + 2x2 + -2x2 Combine like terms: -10x + 10x = 0 8 + 14x + -2x2 = 0 + 2x2 + -2x2 8 + 14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + 14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + -1x2 = 0 Solving 4 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -7x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -7x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -7x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7x + x2 = 0 + 4 -7x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7x + x2 = 4 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 4 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + -7x + x2 = 16.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -3.5 = 4.031128874 Simplifying x + -3.5 = 4.031128874 Reorder the terms: -3.5 + x = 4.031128874 Solving -3.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.031128874 + 3.5 x = 4.031128874 + 3.5 Combine like terms: 4.031128874 + 3.5 = 7.531128874 x = 7.531128874 Simplifying x = 7.531128874Subproblem 2
x + -3.5 = -4.031128874 Simplifying x + -3.5 = -4.031128874 Reorder the terms: -3.5 + x = -4.031128874 Solving -3.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.031128874 + 3.5 x = -4.031128874 + 3.5 Combine like terms: -4.031128874 + 3.5 = -0.531128874 x = -0.531128874 Simplifying x = -0.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.531128874, -0.531128874}Solution
x = {7.531128874, -0.531128874}
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