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Simplifying -1x2 + 32x = -9 Reorder the terms: 32x + -1x2 = -9 Solving 32x + -1x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + 32x + -1x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -32x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -32x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -32x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -32x + x2 = 0 + 9 -32x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -32x + x2 = 9 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 = 9 + 256 Reorder the terms: 256 + -32x + x2 = 9 + 256 Combine like terms: 9 + 256 = 265 256 + -32x + x2 = 265 Factor a perfect square on the left side: (x + -16)(x + -16) = 265 Calculate the square root of the right side: 16.278820596 Break this problem into two subproblems by setting (x + -16) equal to 16.278820596 and -16.278820596.Subproblem 1
x + -16 = 16.278820596 Simplifying x + -16 = 16.278820596 Reorder the terms: -16 + x = 16.278820596 Solving -16 + x = 16.278820596 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 = 16.278820596 + 16 Combine like terms: -16 + 16 = 0 0 + x = 16.278820596 + 16 x = 16.278820596 + 16 Combine like terms: 16.278820596 + 16 = 32.278820596 x = 32.278820596 Simplifying x = 32.278820596Subproblem 2
x + -16 = -16.278820596 Simplifying x + -16 = -16.278820596 Reorder the terms: -16 + x = -16.278820596 Solving -16 + x = -16.278820596 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 = -16.278820596 + 16 Combine like terms: -16 + 16 = 0 0 + x = -16.278820596 + 16 x = -16.278820596 + 16 Combine like terms: -16.278820596 + 16 = -0.278820596 x = -0.278820596 Simplifying x = -0.278820596Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.278820596, -0.278820596}
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