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Simplifying x2 + 116x + -64 = 0 Reorder the terms: -64 + 116x + x2 = 0 Solving -64 + 116x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 116x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 116x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 116x + x2 = 0 + 64 116x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 116x + x2 = 64 The x term is 116x. Take half its coefficient (58). Square it (3364) and add it to both sides. Add '3364' to each side of the equation. 116x + 3364 + x2 = 64 + 3364 Reorder the terms: 3364 + 116x + x2 = 64 + 3364 Combine like terms: 64 + 3364 = 3428 3364 + 116x + x2 = 3428 Factor a perfect square on the left side: (x + 58)(x + 58) = 3428 Calculate the square root of the right side: 58.549124673 Break this problem into two subproblems by setting (x + 58) equal to 58.549124673 and -58.549124673.Subproblem 1
x + 58 = 58.549124673 Simplifying x + 58 = 58.549124673 Reorder the terms: 58 + x = 58.549124673 Solving 58 + x = 58.549124673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58' to each side of the equation. 58 + -58 + x = 58.549124673 + -58 Combine like terms: 58 + -58 = 0 0 + x = 58.549124673 + -58 x = 58.549124673 + -58 Combine like terms: 58.549124673 + -58 = 0.549124673 x = 0.549124673 Simplifying x = 0.549124673Subproblem 2
x + 58 = -58.549124673 Simplifying x + 58 = -58.549124673 Reorder the terms: 58 + x = -58.549124673 Solving 58 + x = -58.549124673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58' to each side of the equation. 58 + -58 + x = -58.549124673 + -58 Combine like terms: 58 + -58 = 0 0 + x = -58.549124673 + -58 x = -58.549124673 + -58 Combine like terms: -58.549124673 + -58 = -116.549124673 x = -116.549124673 Simplifying x = -116.549124673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.549124673, -116.549124673}
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