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Simplifying x2 + 32x + 2 = 0 Reorder the terms: 2 + 32x + x2 = 0 Solving 2 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 32x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 32x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 32x + x2 = 0 + -2 32x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 32x + x2 = -2 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 = -2 + 256 Reorder the terms: 256 + 32x + x2 = -2 + 256 Combine like terms: -2 + 256 = 254 256 + 32x + x2 = 254 Factor a perfect square on the left side: (x + 16)(x + 16) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (x + 16) equal to 15.937377451 and -15.937377451.Subproblem 1
x + 16 = 15.937377451 Simplifying x + 16 = 15.937377451 Reorder the terms: 16 + x = 15.937377451 Solving 16 + x = 15.937377451 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 = 15.937377451 + -16 Combine like terms: 16 + -16 = 0 0 + x = 15.937377451 + -16 x = 15.937377451 + -16 Combine like terms: 15.937377451 + -16 = -0.062622549 x = -0.062622549 Simplifying x = -0.062622549Subproblem 2
x + 16 = -15.937377451 Simplifying x + 16 = -15.937377451 Reorder the terms: 16 + x = -15.937377451 Solving 16 + x = -15.937377451 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 = -15.937377451 + -16 Combine like terms: 16 + -16 = 0 0 + x = -15.937377451 + -16 x = -15.937377451 + -16 Combine like terms: -15.937377451 + -16 = -31.937377451 x = -31.937377451 Simplifying x = -31.937377451Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.062622549, -31.937377451}
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