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Simplifying 9x + 64 = x2 + 26x + 12 Reorder the terms: 64 + 9x = x2 + 26x + 12 Reorder the terms: 64 + 9x = 12 + 26x + x2 Solving 64 + 9x = 12 + 26x + x2 Solving for variable 'x'. Reorder the terms: 64 + -12 + 9x + -26x + -1x2 = 12 + 26x + x2 + -12 + -26x + -1x2 Combine like terms: 64 + -12 = 52 52 + 9x + -26x + -1x2 = 12 + 26x + x2 + -12 + -26x + -1x2 Combine like terms: 9x + -26x = -17x 52 + -17x + -1x2 = 12 + 26x + x2 + -12 + -26x + -1x2 Reorder the terms: 52 + -17x + -1x2 = 12 + -12 + 26x + -26x + x2 + -1x2 Combine like terms: 12 + -12 = 0 52 + -17x + -1x2 = 0 + 26x + -26x + x2 + -1x2 52 + -17x + -1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 52 + -17x + -1x2 = 0 + x2 + -1x2 52 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 52 + -17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -52 + 17x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + 17x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 17x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 17x + x2 = 0 + 52 17x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 17x + x2 = 52 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 52 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 52 + 72.25 Combine like terms: 52 + 72.25 = 124.25 72.25 + 17x + x2 = 124.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + 8.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + 8.5 = 11.146748405 Simplifying x + 8.5 = 11.146748405 Reorder the terms: 8.5 + x = 11.146748405 Solving 8.5 + x = 11.146748405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 11.146748405 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 11.146748405 + -8.5 x = 11.146748405 + -8.5 Combine like terms: 11.146748405 + -8.5 = 2.646748405 x = 2.646748405 Simplifying x = 2.646748405Subproblem 2
x + 8.5 = -11.146748405 Simplifying x + 8.5 = -11.146748405 Reorder the terms: 8.5 + x = -11.146748405 Solving 8.5 + x = -11.146748405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -11.146748405 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -11.146748405 + -8.5 x = -11.146748405 + -8.5 Combine like terms: -11.146748405 + -8.5 = -19.646748405 x = -19.646748405 Simplifying x = -19.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.646748405, -19.646748405}
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