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Simplifying 1152 = 2x2 + 8x + -64 Reorder the terms: 1152 = -64 + 8x + 2x2 Solving 1152 = -64 + 8x + 2x2 Solving for variable 'x'. Combine like terms: 1152 + 64 = 1216 1216 + -8x + -2x2 = -64 + 8x + 2x2 + 64 + -8x + -2x2 Reorder the terms: 1216 + -8x + -2x2 = -64 + 64 + 8x + -8x + 2x2 + -2x2 Combine like terms: -64 + 64 = 0 1216 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 1216 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 1216 + -8x + -2x2 = 0 + 2x2 + -2x2 1216 + -8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1216 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(608 + -4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(608 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 608 + -4x + -1x2 = 0 Solving 608 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -608 + 4x + x2 = 0 Move the constant term to the right: Add '608' to each side of the equation. -608 + 4x + 608 + x2 = 0 + 608 Reorder the terms: -608 + 608 + 4x + x2 = 0 + 608 Combine like terms: -608 + 608 = 0 0 + 4x + x2 = 0 + 608 4x + x2 = 0 + 608 Combine like terms: 0 + 608 = 608 4x + x2 = 608 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 608 + 4 Reorder the terms: 4 + 4x + x2 = 608 + 4 Combine like terms: 608 + 4 = 612 4 + 4x + x2 = 612 Factor a perfect square on the left side: (x + 2)(x + 2) = 612 Calculate the square root of the right side: 24.738633754 Break this problem into two subproblems by setting (x + 2) equal to 24.738633754 and -24.738633754.Subproblem 1
x + 2 = 24.738633754 Simplifying x + 2 = 24.738633754 Reorder the terms: 2 + x = 24.738633754 Solving 2 + x = 24.738633754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 24.738633754 + -2 Combine like terms: 2 + -2 = 0 0 + x = 24.738633754 + -2 x = 24.738633754 + -2 Combine like terms: 24.738633754 + -2 = 22.738633754 x = 22.738633754 Simplifying x = 22.738633754Subproblem 2
x + 2 = -24.738633754 Simplifying x + 2 = -24.738633754 Reorder the terms: 2 + x = -24.738633754 Solving 2 + x = -24.738633754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -24.738633754 + -2 Combine like terms: 2 + -2 = 0 0 + x = -24.738633754 + -2 x = -24.738633754 + -2 Combine like terms: -24.738633754 + -2 = -26.738633754 x = -26.738633754 Simplifying x = -26.738633754Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.738633754, -26.738633754}Solution
x = {22.738633754, -26.738633754}
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