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Simplifying 1080 = 2x2 + 8x + 64 Reorder the terms: 1080 = 64 + 8x + 2x2 Solving 1080 = 64 + 8x + 2x2 Solving for variable 'x'. Combine like terms: 1080 + -64 = 1016 1016 + -8x + -2x2 = 64 + 8x + 2x2 + -64 + -8x + -2x2 Reorder the terms: 1016 + -8x + -2x2 = 64 + -64 + 8x + -8x + 2x2 + -2x2 Combine like terms: 64 + -64 = 0 1016 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 1016 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 1016 + -8x + -2x2 = 0 + 2x2 + -2x2 1016 + -8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1016 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(508 + -4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(508 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 508 + -4x + -1x2 = 0 Solving 508 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -508 + 4x + x2 = 0 Move the constant term to the right: Add '508' to each side of the equation. -508 + 4x + 508 + x2 = 0 + 508 Reorder the terms: -508 + 508 + 4x + x2 = 0 + 508 Combine like terms: -508 + 508 = 0 0 + 4x + x2 = 0 + 508 4x + x2 = 0 + 508 Combine like terms: 0 + 508 = 508 4x + x2 = 508 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 = 508 + 4 Reorder the terms: 4 + 4x + x2 = 508 + 4 Combine like terms: 508 + 4 = 512 4 + 4x + x2 = 512 Factor a perfect square on the left side: (x + 2)(x + 2) = 512 Calculate the square root of the right side: 22.627416998 Break this problem into two subproblems by setting (x + 2) equal to 22.627416998 and -22.627416998.Subproblem 1
x + 2 = 22.627416998 Simplifying x + 2 = 22.627416998 Reorder the terms: 2 + x = 22.627416998 Solving 2 + x = 22.627416998 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 = 22.627416998 + -2 Combine like terms: 2 + -2 = 0 0 + x = 22.627416998 + -2 x = 22.627416998 + -2 Combine like terms: 22.627416998 + -2 = 20.627416998 x = 20.627416998 Simplifying x = 20.627416998Subproblem 2
x + 2 = -22.627416998 Simplifying x + 2 = -22.627416998 Reorder the terms: 2 + x = -22.627416998 Solving 2 + x = -22.627416998 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 = -22.627416998 + -2 Combine like terms: 2 + -2 = 0 0 + x = -22.627416998 + -2 x = -22.627416998 + -2 Combine like terms: -22.627416998 + -2 = -24.627416998 x = -24.627416998 Simplifying x = -24.627416998Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.627416998, -24.627416998}Solution
x = {20.627416998, -24.627416998}
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