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Simplifying (x + -9)(x + -8) = 5x + 37 Reorder the terms: (-9 + x)(x + -8) = 5x + 37 Reorder the terms: (-9 + x)(-8 + x) = 5x + 37 Multiply (-9 + x) * (-8 + x) (-9(-8 + x) + x(-8 + x)) = 5x + 37 ((-8 * -9 + x * -9) + x(-8 + x)) = 5x + 37 ((72 + -9x) + x(-8 + x)) = 5x + 37 (72 + -9x + (-8 * x + x * x)) = 5x + 37 (72 + -9x + (-8x + x2)) = 5x + 37 Combine like terms: -9x + -8x = -17x (72 + -17x + x2) = 5x + 37 Reorder the terms: 72 + -17x + x2 = 37 + 5x Solving 72 + -17x + x2 = 37 + 5x Solving for variable 'x'. Reorder the terms: 72 + -37 + -17x + -5x + x2 = 37 + 5x + -37 + -5x Combine like terms: 72 + -37 = 35 35 + -17x + -5x + x2 = 37 + 5x + -37 + -5x Combine like terms: -17x + -5x = -22x 35 + -22x + x2 = 37 + 5x + -37 + -5x Reorder the terms: 35 + -22x + x2 = 37 + -37 + 5x + -5x Combine like terms: 37 + -37 = 0 35 + -22x + x2 = 0 + 5x + -5x 35 + -22x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 35 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -22x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -22x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -22x + x2 = 0 + -35 -22x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -22x + x2 = -35 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 = -35 + 121 Reorder the terms: 121 + -22x + x2 = -35 + 121 Combine like terms: -35 + 121 = 86 121 + -22x + x2 = 86 Factor a perfect square on the left side: (x + -11)(x + -11) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -11) equal to 9.273618495 and -9.273618495.Subproblem 1
x + -11 = 9.273618495 Simplifying x + -11 = 9.273618495 Reorder the terms: -11 + x = 9.273618495 Solving -11 + x = 9.273618495 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 = 9.273618495 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.273618495 + 11 x = 9.273618495 + 11 Combine like terms: 9.273618495 + 11 = 20.273618495 x = 20.273618495 Simplifying x = 20.273618495Subproblem 2
x + -11 = -9.273618495 Simplifying x + -11 = -9.273618495 Reorder the terms: -11 + x = -9.273618495 Solving -11 + x = -9.273618495 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 = -9.273618495 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.273618495 + 11 x = -9.273618495 + 11 Combine like terms: -9.273618495 + 11 = 1.726381505 x = 1.726381505 Simplifying x = 1.726381505Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.273618495, 1.726381505}
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