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Simplifying (x + -11)(2x + -7) = 180 Reorder the terms: (-11 + x)(2x + -7) = 180 Reorder the terms: (-11 + x)(-7 + 2x) = 180 Multiply (-11 + x) * (-7 + 2x) (-11(-7 + 2x) + x(-7 + 2x)) = 180 ((-7 * -11 + 2x * -11) + x(-7 + 2x)) = 180 ((77 + -22x) + x(-7 + 2x)) = 180 (77 + -22x + (-7 * x + 2x * x)) = 180 (77 + -22x + (-7x + 2x2)) = 180 Combine like terms: -22x + -7x = -29x (77 + -29x + 2x2) = 180 Solving 77 + -29x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 77 + -180 + -29x + 2x2 = 180 + -180 Combine like terms: 77 + -180 = -103 -103 + -29x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -103 + -29x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -51.5 + -14.5x + x2 = 0 Move the constant term to the right: Add '51.5' to each side of the equation. -51.5 + -14.5x + 51.5 + x2 = 0 + 51.5 Reorder the terms: -51.5 + 51.5 + -14.5x + x2 = 0 + 51.5 Combine like terms: -51.5 + 51.5 = 0.0 0.0 + -14.5x + x2 = 0 + 51.5 -14.5x + x2 = 0 + 51.5 Combine like terms: 0 + 51.5 = 51.5 -14.5x + x2 = 51.5 The x term is -14.5x. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5x + 52.5625 + x2 = 51.5 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = 51.5 + 52.5625 Combine like terms: 51.5 + 52.5625 = 104.0625 52.5625 + -14.5x + x2 = 104.0625 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 104.0625 Calculate the square root of the right side: 10.201102882 Break this problem into two subproblems by setting (x + -7.25) equal to 10.201102882 and -10.201102882.Subproblem 1
x + -7.25 = 10.201102882 Simplifying x + -7.25 = 10.201102882 Reorder the terms: -7.25 + x = 10.201102882 Solving -7.25 + x = 10.201102882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 10.201102882 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 10.201102882 + 7.25 x = 10.201102882 + 7.25 Combine like terms: 10.201102882 + 7.25 = 17.451102882 x = 17.451102882 Simplifying x = 17.451102882Subproblem 2
x + -7.25 = -10.201102882 Simplifying x + -7.25 = -10.201102882 Reorder the terms: -7.25 + x = -10.201102882 Solving -7.25 + x = -10.201102882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -10.201102882 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -10.201102882 + 7.25 x = -10.201102882 + 7.25 Combine like terms: -10.201102882 + 7.25 = -2.951102882 x = -2.951102882 Simplifying x = -2.951102882Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.451102882, -2.951102882}
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