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Simplifying (5x + 6)(x + -1) + -1(2x2 + -5x + -3) = 0 Reorder the terms: (6 + 5x)(x + -1) + -1(2x2 + -5x + -3) = 0 Reorder the terms: (6 + 5x)(-1 + x) + -1(2x2 + -5x + -3) = 0 Multiply (6 + 5x) * (-1 + x) (6(-1 + x) + 5x * (-1 + x)) + -1(2x2 + -5x + -3) = 0 ((-1 * 6 + x * 6) + 5x * (-1 + x)) + -1(2x2 + -5x + -3) = 0 ((-6 + 6x) + 5x * (-1 + x)) + -1(2x2 + -5x + -3) = 0 (-6 + 6x + (-1 * 5x + x * 5x)) + -1(2x2 + -5x + -3) = 0 (-6 + 6x + (-5x + 5x2)) + -1(2x2 + -5x + -3) = 0 Combine like terms: 6x + -5x = 1x (-6 + 1x + 5x2) + -1(2x2 + -5x + -3) = 0 Reorder the terms: -6 + 1x + 5x2 + -1(-3 + -5x + 2x2) = 0 -6 + 1x + 5x2 + (-3 * -1 + -5x * -1 + 2x2 * -1) = 0 -6 + 1x + 5x2 + (3 + 5x + -2x2) = 0 Reorder the terms: -6 + 3 + 1x + 5x + 5x2 + -2x2 = 0 Combine like terms: -6 + 3 = -3 -3 + 1x + 5x + 5x2 + -2x2 = 0 Combine like terms: 1x + 5x = 6x -3 + 6x + 5x2 + -2x2 = 0 Combine like terms: 5x2 + -2x2 = 3x2 -3 + 6x + 3x2 = 0 Solving -3 + 6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 2x + x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + x2 = 0 Solving -1 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x + x2 = 0 + 1 2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2x + x2 = 1 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1 + 1 Reorder the terms: 1 + 2x + x2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2x + x2 = 2 Factor a perfect square on the left side: (x + 1)(x + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 1 = 1.414213562 Simplifying x + 1 = 1.414213562 Reorder the terms: 1 + x = 1.414213562 Solving 1 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.414213562 + -1 x = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 x = 0.414213562 Simplifying x = 0.414213562Subproblem 2
x + 1 = -1.414213562 Simplifying x + 1 = -1.414213562 Reorder the terms: 1 + x = -1.414213562 Solving 1 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.414213562 + -1 x = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 x = -2.414213562 Simplifying x = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.414213562, -2.414213562}Solution
x = {0.414213562, -2.414213562}
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