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Simplifying 126 = (x + 3)(x)(1) Reorder the terms: 126 = (3 + x)(x)(1) Reorder the terms for easier multiplication: 126 = 1x(3 + x) 126 = (3 * 1x + x * 1x) 126 = (3x + 1x2) Solving 126 = 3x + 1x2 Solving for variable 'x'. Reorder the terms: 126 + -3x + -1x2 = 3x + -3x + 1x2 + -1x2 Combine like terms: 3x + -3x = 0 126 + -3x + -1x2 = 0 + 1x2 + -1x2 126 + -3x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 126 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -126 + 3x + x2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + 3x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 3x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 3x + x2 = 0 + 126 3x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 3x + x2 = 126 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 126 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 126 + 2.25 Combine like terms: 126 + 2.25 = 128.25 2.25 + 3x + x2 = 128.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + 1.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + 1.5 = 11.324751653 Simplifying x + 1.5 = 11.324751653 Reorder the terms: 1.5 + x = 11.324751653 Solving 1.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.324751653 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.324751653 + -1.5 x = 11.324751653 + -1.5 Combine like terms: 11.324751653 + -1.5 = 9.824751653 x = 9.824751653 Simplifying x = 9.824751653Subproblem 2
x + 1.5 = -11.324751653 Simplifying x + 1.5 = -11.324751653 Reorder the terms: 1.5 + x = -11.324751653 Solving 1.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.324751653 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.324751653 + -1.5 x = -11.324751653 + -1.5 Combine like terms: -11.324751653 + -1.5 = -12.824751653 x = -12.824751653 Simplifying x = -12.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.824751653, -12.824751653}
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