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Simplifying 0 = x2 + -32x + -5 Reorder the terms: 0 = -5 + -32x + x2 Solving 0 = -5 + -32x + x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + 32x + -1x2 = -5 + -32x + x2 + 5 + 32x + -1x2 Reorder the terms: 5 + 32x + -1x2 = -5 + 5 + -32x + 32x + x2 + -1x2 Combine like terms: -5 + 5 = 0 5 + 32x + -1x2 = 0 + -32x + 32x + x2 + -1x2 5 + 32x + -1x2 = -32x + 32x + x2 + -1x2 Combine like terms: -32x + 32x = 0 5 + 32x + -1x2 = 0 + x2 + -1x2 5 + 32x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -32x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -32x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -32x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -32x + x2 = 0 + 5 -32x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -32x + x2 = 5 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 = 5 + 256 Reorder the terms: 256 + -32x + x2 = 5 + 256 Combine like terms: 5 + 256 = 261 256 + -32x + x2 = 261 Factor a perfect square on the left side: (x + -16)(x + -16) = 261 Calculate the square root of the right side: 16.155494421 Break this problem into two subproblems by setting (x + -16) equal to 16.155494421 and -16.155494421.Subproblem 1
x + -16 = 16.155494421 Simplifying x + -16 = 16.155494421 Reorder the terms: -16 + x = 16.155494421 Solving -16 + x = 16.155494421 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 = 16.155494421 + 16 Combine like terms: -16 + 16 = 0 0 + x = 16.155494421 + 16 x = 16.155494421 + 16 Combine like terms: 16.155494421 + 16 = 32.155494421 x = 32.155494421 Simplifying x = 32.155494421Subproblem 2
x + -16 = -16.155494421 Simplifying x + -16 = -16.155494421 Reorder the terms: -16 + x = -16.155494421 Solving -16 + x = -16.155494421 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 = -16.155494421 + 16 Combine like terms: -16 + 16 = 0 0 + x = -16.155494421 + 16 x = -16.155494421 + 16 Combine like terms: -16.155494421 + 16 = -0.155494421 x = -0.155494421 Simplifying x = -0.155494421Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.155494421, -0.155494421}
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