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Simplifying 2x2 + 32x + -144 = 0 Reorder the terms: -144 + 32x + 2x2 = 0 Solving -144 + 32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + 16x + x2)' equal to zero and attempt to solve: Simplifying -72 + 16x + x2 = 0 Solving -72 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 16x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 16x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 16x + x2 = 0 + 72 16x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 16x + x2 = 72 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 = 72 + 64 Reorder the terms: 64 + 16x + x2 = 72 + 64 Combine like terms: 72 + 64 = 136 64 + 16x + x2 = 136 Factor a perfect square on the left side: (x + 8)(x + 8) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + 8) equal to 11.66190379 and -11.66190379.Subproblem 1
x + 8 = 11.66190379 Simplifying x + 8 = 11.66190379 Reorder the terms: 8 + x = 11.66190379 Solving 8 + x = 11.66190379 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 = 11.66190379 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.66190379 + -8 x = 11.66190379 + -8 Combine like terms: 11.66190379 + -8 = 3.66190379 x = 3.66190379 Simplifying x = 3.66190379Subproblem 2
x + 8 = -11.66190379 Simplifying x + 8 = -11.66190379 Reorder the terms: 8 + x = -11.66190379 Solving 8 + x = -11.66190379 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 = -11.66190379 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.66190379 + -8 x = -11.66190379 + -8 Combine like terms: -11.66190379 + -8 = -19.66190379 x = -19.66190379 Simplifying x = -19.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.66190379, -19.66190379}Solution
x = {3.66190379, -19.66190379}
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