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Simplifying (x + -9)(x + -13) = 53 Reorder the terms: (-9 + x)(x + -13) = 53 Reorder the terms: (-9 + x)(-13 + x) = 53 Multiply (-9 + x) * (-13 + x) (-9(-13 + x) + x(-13 + x)) = 53 ((-13 * -9 + x * -9) + x(-13 + x)) = 53 ((117 + -9x) + x(-13 + x)) = 53 (117 + -9x + (-13 * x + x * x)) = 53 (117 + -9x + (-13x + x2)) = 53 Combine like terms: -9x + -13x = -22x (117 + -22x + x2) = 53 Solving 117 + -22x + x2 = 53 Solving for variable 'x'. Reorder the terms: 117 + -53 + -22x + x2 = 53 + -53 Combine like terms: 117 + -53 = 64 64 + -22x + x2 = 53 + -53 Combine like terms: 53 + -53 = 0 64 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -22x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -22x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -22x + x2 = 0 + -64 -22x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -22x + x2 = -64 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -64 + 121 Reorder the terms: 121 + -22x + x2 = -64 + 121 Combine like terms: -64 + 121 = 57 121 + -22x + x2 = 57 Factor a perfect square on the left side: (x + -11)(x + -11) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -11) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -11 = 7.549834435 Simplifying x + -11 = 7.549834435 Reorder the terms: -11 + x = 7.549834435 Solving -11 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 7.549834435 + 11 Combine like terms: -11 + 11 = 0 0 + x = 7.549834435 + 11 x = 7.549834435 + 11 Combine like terms: 7.549834435 + 11 = 18.549834435 x = 18.549834435 Simplifying x = 18.549834435Subproblem 2
x + -11 = -7.549834435 Simplifying x + -11 = -7.549834435 Reorder the terms: -11 + x = -7.549834435 Solving -11 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -7.549834435 + 11 Combine like terms: -11 + 11 = 0 0 + x = -7.549834435 + 11 x = -7.549834435 + 11 Combine like terms: -7.549834435 + 11 = 3.450165565 x = 3.450165565 Simplifying x = 3.450165565Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.549834435, 3.450165565}
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