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Simplifying (x)(x + -2) = (9)(x + 4) Reorder the terms: x(-2 + x) = (9)(x + 4) (-2 * x + x * x) = (9)(x + 4) (-2x + x2) = (9)(x + 4) Reorder the terms: -2x + x2 = 9(4 + x) -2x + x2 = (4 * 9 + x * 9) -2x + x2 = (36 + 9x) Solving -2x + x2 = 36 + 9x Solving for variable 'x'. Reorder the terms: -36 + -2x + -9x + x2 = 36 + 9x + -36 + -9x Combine like terms: -2x + -9x = -11x -36 + -11x + x2 = 36 + 9x + -36 + -9x Reorder the terms: -36 + -11x + x2 = 36 + -36 + 9x + -9x Combine like terms: 36 + -36 = 0 -36 + -11x + x2 = 0 + 9x + -9x -36 + -11x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -36 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -11x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -11x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -11x + x2 = 0 + 36 -11x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -11x + x2 = 36 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 36 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 36 + 30.25 Combine like terms: 36 + 30.25 = 66.25 30.25 + -11x + x2 = 66.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + -5.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + -5.5 = 8.139410298 Simplifying x + -5.5 = 8.139410298 Reorder the terms: -5.5 + x = 8.139410298 Solving -5.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 8.139410298 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.139410298 + 5.5 x = 8.139410298 + 5.5 Combine like terms: 8.139410298 + 5.5 = 13.639410298 x = 13.639410298 Simplifying x = 13.639410298Subproblem 2
x + -5.5 = -8.139410298 Simplifying x + -5.5 = -8.139410298 Reorder the terms: -5.5 + x = -8.139410298 Solving -5.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -8.139410298 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.139410298 + 5.5 x = -8.139410298 + 5.5 Combine like terms: -8.139410298 + 5.5 = -2.639410298 x = -2.639410298 Simplifying x = -2.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.639410298, -2.639410298}
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