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Simplifying -2x2 + -32x = 52 Reorder the terms: -32x + -2x2 = 52 Solving -32x + -2x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + -32x + -2x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + -32x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(26 + 16x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(26 + 16x + x2)' equal to zero and attempt to solve: Simplifying 26 + 16x + x2 = 0 Solving 26 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 16x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + 16x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 16x + x2 = 0 + -26 16x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 16x + x2 = -26 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -26 + 64 Reorder the terms: 64 + 16x + x2 = -26 + 64 Combine like terms: -26 + 64 = 38 64 + 16x + x2 = 38 Factor a perfect square on the left side: (x + 8)(x + 8) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 8) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 8 = 6.164414003 Simplifying x + 8 = 6.164414003 Reorder the terms: 8 + x = 6.164414003 Solving 8 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 6.164414003 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.164414003 + -8 x = 6.164414003 + -8 Combine like terms: 6.164414003 + -8 = -1.835585997 x = -1.835585997 Simplifying x = -1.835585997Subproblem 2
x + 8 = -6.164414003 Simplifying x + 8 = -6.164414003 Reorder the terms: 8 + x = -6.164414003 Solving 8 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -6.164414003 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.164414003 + -8 x = -6.164414003 + -8 Combine like terms: -6.164414003 + -8 = -14.164414003 x = -14.164414003 Simplifying x = -14.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.835585997, -14.164414003}Solution
x = {-1.835585997, -14.164414003}
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