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Simplifying x2 + 4x = 126 Reorder the terms: 4x + x2 = 126 Solving 4x + x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 4x + x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + 4x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 4x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 4x + x2 = 0 + 126 4x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 4x + x2 = 126 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 = 126 + 4 Reorder the terms: 4 + 4x + x2 = 126 + 4 Combine like terms: 126 + 4 = 130 4 + 4x + x2 = 130 Factor a perfect square on the left side: (x + 2)(x + 2) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 2) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 2 = 11.401754251 Simplifying x + 2 = 11.401754251 Reorder the terms: 2 + x = 11.401754251 Solving 2 + x = 11.401754251 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 = 11.401754251 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.401754251 + -2 x = 11.401754251 + -2 Combine like terms: 11.401754251 + -2 = 9.401754251 x = 9.401754251 Simplifying x = 9.401754251Subproblem 2
x + 2 = -11.401754251 Simplifying x + 2 = -11.401754251 Reorder the terms: 2 + x = -11.401754251 Solving 2 + x = -11.401754251 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 = -11.401754251 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.401754251 + -2 x = -11.401754251 + -2 Combine like terms: -11.401754251 + -2 = -13.401754251 x = -13.401754251 Simplifying x = -13.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.401754251, -13.401754251}
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