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Simplifying 5 + -5x = (3x + 4)(x + 1) Reorder the terms: 5 + -5x = (4 + 3x)(x + 1) Reorder the terms: 5 + -5x = (4 + 3x)(1 + x) Multiply (4 + 3x) * (1 + x) 5 + -5x = (4(1 + x) + 3x * (1 + x)) 5 + -5x = ((1 * 4 + x * 4) + 3x * (1 + x)) 5 + -5x = ((4 + 4x) + 3x * (1 + x)) 5 + -5x = (4 + 4x + (1 * 3x + x * 3x)) 5 + -5x = (4 + 4x + (3x + 3x2)) Combine like terms: 4x + 3x = 7x 5 + -5x = (4 + 7x + 3x2) Solving 5 + -5x = 4 + 7x + 3x2 Solving for variable 'x'. Reorder the terms: 5 + -4 + -5x + -7x + -3x2 = 4 + 7x + 3x2 + -4 + -7x + -3x2 Combine like terms: 5 + -4 = 1 1 + -5x + -7x + -3x2 = 4 + 7x + 3x2 + -4 + -7x + -3x2 Combine like terms: -5x + -7x = -12x 1 + -12x + -3x2 = 4 + 7x + 3x2 + -4 + -7x + -3x2 Reorder the terms: 1 + -12x + -3x2 = 4 + -4 + 7x + -7x + 3x2 + -3x2 Combine like terms: 4 + -4 = 0 1 + -12x + -3x2 = 0 + 7x + -7x + 3x2 + -3x2 1 + -12x + -3x2 = 7x + -7x + 3x2 + -3x2 Combine like terms: 7x + -7x = 0 1 + -12x + -3x2 = 0 + 3x2 + -3x2 1 + -12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 1 + -12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + 4x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 4x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 4x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 4x + x2 = 0 + 0.3333333333 4x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 4x + x2 = 0.3333333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 0.3333333333 + 4 Reorder the terms: 4 + 4x + x2 = 0.3333333333 + 4 Combine like terms: 0.3333333333 + 4 = 4.3333333333 4 + 4x + x2 = 4.3333333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.3333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (x + 2) equal to 2.081665999 and -2.081665999.Subproblem 1
x + 2 = 2.081665999 Simplifying x + 2 = 2.081665999 Reorder the terms: 2 + x = 2.081665999 Solving 2 + x = 2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.081665999 + -2 x = 2.081665999 + -2 Combine like terms: 2.081665999 + -2 = 0.081665999 x = 0.081665999 Simplifying x = 0.081665999Subproblem 2
x + 2 = -2.081665999 Simplifying x + 2 = -2.081665999 Reorder the terms: 2 + x = -2.081665999 Solving 2 + x = -2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.081665999 + -2 x = -2.081665999 + -2 Combine like terms: -2.081665999 + -2 = -4.081665999 x = -4.081665999 Simplifying x = -4.081665999Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.081665999, -4.081665999}
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