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Simplifying 32x + -9 = x2 Reorder the terms: -9 + 32x = x2 Solving -9 + 32x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 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 = 247 256 + -32x + x2 = 247 Factor a perfect square on the left side: (x + -16)(x + -16) = 247 Calculate the square root of the right side: 15.716233646 Break this problem into two subproblems by setting (x + -16) equal to 15.716233646 and -15.716233646.Subproblem 1
x + -16 = 15.716233646 Simplifying x + -16 = 15.716233646 Reorder the terms: -16 + x = 15.716233646 Solving -16 + x = 15.716233646 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 = 15.716233646 + 16 Combine like terms: -16 + 16 = 0 0 + x = 15.716233646 + 16 x = 15.716233646 + 16 Combine like terms: 15.716233646 + 16 = 31.716233646 x = 31.716233646 Simplifying x = 31.716233646Subproblem 2
x + -16 = -15.716233646 Simplifying x + -16 = -15.716233646 Reorder the terms: -16 + x = -15.716233646 Solving -16 + x = -15.716233646 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 = -15.716233646 + 16 Combine like terms: -16 + 16 = 0 0 + x = -15.716233646 + 16 x = -15.716233646 + 16 Combine like terms: -15.716233646 + 16 = 0.283766354 x = 0.283766354 Simplifying x = 0.283766354Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.716233646, 0.283766354}
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