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Simplifying 2(x + 9)(x + -2) + -1x(x + 9) = 144 Reorder the terms: 2(9 + x)(x + -2) + -1x(x + 9) = 144 Reorder the terms: 2(9 + x)(-2 + x) + -1x(x + 9) = 144 Multiply (9 + x) * (-2 + x) 2(9(-2 + x) + x(-2 + x)) + -1x(x + 9) = 144 2((-2 * 9 + x * 9) + x(-2 + x)) + -1x(x + 9) = 144 2((-18 + 9x) + x(-2 + x)) + -1x(x + 9) = 144 2(-18 + 9x + (-2 * x + x * x)) + -1x(x + 9) = 144 2(-18 + 9x + (-2x + x2)) + -1x(x + 9) = 144 Combine like terms: 9x + -2x = 7x 2(-18 + 7x + x2) + -1x(x + 9) = 144 (-18 * 2 + 7x * 2 + x2 * 2) + -1x(x + 9) = 144 (-36 + 14x + 2x2) + -1x(x + 9) = 144 Reorder the terms: -36 + 14x + 2x2 + -1x(9 + x) = 144 -36 + 14x + 2x2 + (9 * -1x + x * -1x) = 144 -36 + 14x + 2x2 + (-9x + -1x2) = 144 Reorder the terms: -36 + 14x + -9x + 2x2 + -1x2 = 144 Combine like terms: 14x + -9x = 5x -36 + 5x + 2x2 + -1x2 = 144 Combine like terms: 2x2 + -1x2 = 1x2 -36 + 5x + 1x2 = 144 Solving -36 + 5x + 1x2 = 144 Solving for variable 'x'. Reorder the terms: -36 + -144 + 5x + 1x2 = 144 + -144 Combine like terms: -36 + -144 = -180 -180 + 5x + 1x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -180 + 5x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 5x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 5x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 5x + x2 = 0 + 180 5x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 5x + x2 = 180 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 180 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 180 + 6.25 Combine like terms: 180 + 6.25 = 186.25 6.25 + 5x + x2 = 186.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + 2.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + 2.5 = 13.647344064 Simplifying x + 2.5 = 13.647344064 Reorder the terms: 2.5 + x = 13.647344064 Solving 2.5 + x = 13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.647344064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.647344064 + -2.5 x = 13.647344064 + -2.5 Combine like terms: 13.647344064 + -2.5 = 11.147344064 x = 11.147344064 Simplifying x = 11.147344064Subproblem 2
x + 2.5 = -13.647344064 Simplifying x + 2.5 = -13.647344064 Reorder the terms: 2.5 + x = -13.647344064 Solving 2.5 + x = -13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.647344064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.647344064 + -2.5 x = -13.647344064 + -2.5 Combine like terms: -13.647344064 + -2.5 = -16.147344064 x = -16.147344064 Simplifying x = -16.147344064Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.147344064, -16.147344064}
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