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Simplifying -9x2 + 72x + 288 = 0 Reorder the terms: 288 + 72x + -9x2 = 0 Solving 288 + 72x + -9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(32 + 8x + -1x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(32 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying 32 + 8x + -1x2 = 0 Solving 32 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + -8x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -8x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -8x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -8x + x2 = 0 + 32 -8x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -8x + x2 = 32 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 32 + 16 Reorder the terms: 16 + -8x + x2 = 32 + 16 Combine like terms: 32 + 16 = 48 16 + -8x + x2 = 48 Factor a perfect square on the left side: (x + -4)(x + -4) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -4) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -4 = 6.92820323 Simplifying x + -4 = 6.92820323 Reorder the terms: -4 + x = 6.92820323 Solving -4 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.92820323 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.92820323 + 4 x = 6.92820323 + 4 Combine like terms: 6.92820323 + 4 = 10.92820323 x = 10.92820323 Simplifying x = 10.92820323Subproblem 2
x + -4 = -6.92820323 Simplifying x + -4 = -6.92820323 Reorder the terms: -4 + x = -6.92820323 Solving -4 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.92820323 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.92820323 + 4 x = -6.92820323 + 4 Combine like terms: -6.92820323 + 4 = -2.92820323 x = -2.92820323 Simplifying x = -2.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.92820323, -2.92820323}Solution
x = {10.92820323, -2.92820323}
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