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Simplifying 64 = 9x + x2 Solving 64 = 9x + x2 Solving for variable 'x'. Reorder the terms: 64 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 64 + -9x + -1x2 = 0 + x2 + -1x2 64 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 64 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 9x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 9x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 9x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 9x + x2 = 0 + 64 9x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 9x + x2 = 64 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 64 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 64 + 20.25 Combine like terms: 64 + 20.25 = 84.25 20.25 + 9x + x2 = 84.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 4.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 4.5 = 9.178779875 Simplifying x + 4.5 = 9.178779875 Reorder the terms: 4.5 + x = 9.178779875 Solving 4.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 9.178779875 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.178779875 + -4.5 x = 9.178779875 + -4.5 Combine like terms: 9.178779875 + -4.5 = 4.678779875 x = 4.678779875 Simplifying x = 4.678779875Subproblem 2
x + 4.5 = -9.178779875 Simplifying x + 4.5 = -9.178779875 Reorder the terms: 4.5 + x = -9.178779875 Solving 4.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -9.178779875 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.178779875 + -4.5 x = -9.178779875 + -4.5 Combine like terms: -9.178779875 + -4.5 = -13.678779875 x = -13.678779875 Simplifying x = -13.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.678779875, -13.678779875}
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