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Simplifying x2 + 32x + 13 = 0 Reorder the terms: 13 + 32x + x2 = 0 Solving 13 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 32x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 32x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 32x + x2 = 0 + -13 32x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 32x + x2 = -13 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 = -13 + 256 Reorder the terms: 256 + 32x + x2 = -13 + 256 Combine like terms: -13 + 256 = 243 256 + 32x + x2 = 243 Factor a perfect square on the left side: (x + 16)(x + 16) = 243 Calculate the square root of the right side: 15.588457268 Break this problem into two subproblems by setting (x + 16) equal to 15.588457268 and -15.588457268.Subproblem 1
x + 16 = 15.588457268 Simplifying x + 16 = 15.588457268 Reorder the terms: 16 + x = 15.588457268 Solving 16 + x = 15.588457268 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 = 15.588457268 + -16 Combine like terms: 16 + -16 = 0 0 + x = 15.588457268 + -16 x = 15.588457268 + -16 Combine like terms: 15.588457268 + -16 = -0.411542732 x = -0.411542732 Simplifying x = -0.411542732Subproblem 2
x + 16 = -15.588457268 Simplifying x + 16 = -15.588457268 Reorder the terms: 16 + x = -15.588457268 Solving 16 + x = -15.588457268 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 = -15.588457268 + -16 Combine like terms: 16 + -16 = 0 0 + x = -15.588457268 + -16 x = -15.588457268 + -16 Combine like terms: -15.588457268 + -16 = -31.588457268 x = -31.588457268 Simplifying x = -31.588457268Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.411542732, -31.588457268}
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