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Simplifying 2x2 + 88x + -64 = 0 Reorder the terms: -64 + 88x + 2x2 = 0 Solving -64 + 88x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + 44x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + 44x + x2)' equal to zero and attempt to solve: Simplifying -32 + 44x + x2 = 0 Solving -32 + 44x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 44x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 44x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 44x + x2 = 0 + 32 44x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 44x + x2 = 32 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = 32 + 484 Reorder the terms: 484 + 44x + x2 = 32 + 484 Combine like terms: 32 + 484 = 516 484 + 44x + x2 = 516 Factor a perfect square on the left side: (x + 22)(x + 22) = 516 Calculate the square root of the right side: 22.715633383 Break this problem into two subproblems by setting (x + 22) equal to 22.715633383 and -22.715633383.Subproblem 1
x + 22 = 22.715633383 Simplifying x + 22 = 22.715633383 Reorder the terms: 22 + x = 22.715633383 Solving 22 + x = 22.715633383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 22.715633383 + -22 Combine like terms: 22 + -22 = 0 0 + x = 22.715633383 + -22 x = 22.715633383 + -22 Combine like terms: 22.715633383 + -22 = 0.715633383 x = 0.715633383 Simplifying x = 0.715633383Subproblem 2
x + 22 = -22.715633383 Simplifying x + 22 = -22.715633383 Reorder the terms: 22 + x = -22.715633383 Solving 22 + x = -22.715633383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -22.715633383 + -22 Combine like terms: 22 + -22 = 0 0 + x = -22.715633383 + -22 x = -22.715633383 + -22 Combine like terms: -22.715633383 + -22 = -44.715633383 x = -44.715633383 Simplifying x = -44.715633383Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.715633383, -44.715633383}Solution
x = {0.715633383, -44.715633383}
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