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Simplifying 126 = 2(3 + x + -1)(x + -1) Reorder the terms: 126 = 2(3 + -1 + x)(x + -1) Combine like terms: 3 + -1 = 2 126 = 2(2 + x)(x + -1) Reorder the terms: 126 = 2(2 + x)(-1 + x) Multiply (2 + x) * (-1 + x) 126 = 2(2(-1 + x) + x(-1 + x)) 126 = 2((-1 * 2 + x * 2) + x(-1 + x)) 126 = 2((-2 + 2x) + x(-1 + x)) 126 = 2(-2 + 2x + (-1 * x + x * x)) 126 = 2(-2 + 2x + (-1x + x2)) Combine like terms: 2x + -1x = 1x 126 = 2(-2 + 1x + x2) 126 = (-2 * 2 + 1x * 2 + x2 * 2) 126 = (-4 + 2x + 2x2) Solving 126 = -4 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 126 + 4 = 130 130 + -2x + -2x2 = -4 + 2x + 2x2 + 4 + -2x + -2x2 Reorder the terms: 130 + -2x + -2x2 = -4 + 4 + 2x + -2x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 130 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 130 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 130 + -2x + -2x2 = 0 + 2x2 + -2x2 130 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 130 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(65 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(65 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 65 + -1x + -1x2 = 0 Solving 65 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -65 + x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + x + x2 = 0 + 65 x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 x + x2 = 65 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 65 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 65 + 0.25 Combine like terms: 65 + 0.25 = 65.25 1.25 + x2 = 65.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + 0.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + 0.5 = 8.077747211 Simplifying x + 0.5 = 8.077747211 Reorder the terms: 0.5 + x = 8.077747211 Solving 0.5 + x = 8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.077747211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.077747211 + -0.5 x = 8.077747211 + -0.5 Combine like terms: 8.077747211 + -0.5 = 7.577747211 x = 7.577747211 Simplifying x = 7.577747211Subproblem 2
x + 0.5 = -8.077747211 Simplifying x + 0.5 = -8.077747211 Reorder the terms: 0.5 + x = -8.077747211 Solving 0.5 + x = -8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.077747211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.077747211 + -0.5 x = -8.077747211 + -0.5 Combine like terms: -8.077747211 + -0.5 = -8.577747211 x = -8.577747211 Simplifying x = -8.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.577747211, -8.577747211}Solution
x = {7.577747211, -8.577747211}
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