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Simplifying x2 + 32x + 130 = 0 Reorder the terms: 130 + 32x + x2 = 0 Solving 130 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-130' to each side of the equation. 130 + 32x + -130 + x2 = 0 + -130 Reorder the terms: 130 + -130 + 32x + x2 = 0 + -130 Combine like terms: 130 + -130 = 0 0 + 32x + x2 = 0 + -130 32x + x2 = 0 + -130 Combine like terms: 0 + -130 = -130 32x + x2 = -130 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -130 + 256 Reorder the terms: 256 + 32x + x2 = -130 + 256 Combine like terms: -130 + 256 = 126 256 + 32x + x2 = 126 Factor a perfect square on the left side: (x + 16)(x + 16) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + 16) equal to 11.22497216 and -11.22497216.Subproblem 1
x + 16 = 11.22497216 Simplifying x + 16 = 11.22497216 Reorder the terms: 16 + x = 11.22497216 Solving 16 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 11.22497216 + -16 Combine like terms: 16 + -16 = 0 0 + x = 11.22497216 + -16 x = 11.22497216 + -16 Combine like terms: 11.22497216 + -16 = -4.77502784 x = -4.77502784 Simplifying x = -4.77502784Subproblem 2
x + 16 = -11.22497216 Simplifying x + 16 = -11.22497216 Reorder the terms: 16 + x = -11.22497216 Solving 16 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -11.22497216 + -16 Combine like terms: 16 + -16 = 0 0 + x = -11.22497216 + -16 x = -11.22497216 + -16 Combine like terms: -11.22497216 + -16 = -27.22497216 x = -27.22497216 Simplifying x = -27.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.77502784, -27.22497216}
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