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Simplifying x2 + 32x = -16 Reorder the terms: 32x + x2 = -16 Solving 32x + x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 32x + x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 32x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 32x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 32x + x2 = 0 + -16 32x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 32x + x2 = -16 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 = -16 + 256 Reorder the terms: 256 + 32x + x2 = -16 + 256 Combine like terms: -16 + 256 = 240 256 + 32x + x2 = 240 Factor a perfect square on the left side: (x + 16)(x + 16) = 240 Calculate the square root of the right side: 15.491933385 Break this problem into two subproblems by setting (x + 16) equal to 15.491933385 and -15.491933385.Subproblem 1
x + 16 = 15.491933385 Simplifying x + 16 = 15.491933385 Reorder the terms: 16 + x = 15.491933385 Solving 16 + x = 15.491933385 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 = 15.491933385 + -16 Combine like terms: 16 + -16 = 0 0 + x = 15.491933385 + -16 x = 15.491933385 + -16 Combine like terms: 15.491933385 + -16 = -0.508066615 x = -0.508066615 Simplifying x = -0.508066615Subproblem 2
x + 16 = -15.491933385 Simplifying x + 16 = -15.491933385 Reorder the terms: 16 + x = -15.491933385 Solving 16 + x = -15.491933385 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 = -15.491933385 + -16 Combine like terms: 16 + -16 = 0 0 + x = -15.491933385 + -16 x = -15.491933385 + -16 Combine like terms: -15.491933385 + -16 = -31.491933385 x = -31.491933385 Simplifying x = -31.491933385Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.508066615, -31.491933385}
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