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Simplifying (x + 4)(x + -5) = 180 Reorder the terms: (4 + x)(x + -5) = 180 Reorder the terms: (4 + x)(-5 + x) = 180 Multiply (4 + x) * (-5 + x) (4(-5 + x) + x(-5 + x)) = 180 ((-5 * 4 + x * 4) + x(-5 + x)) = 180 ((-20 + 4x) + x(-5 + x)) = 180 (-20 + 4x + (-5 * x + x * x)) = 180 (-20 + 4x + (-5x + x2)) = 180 Combine like terms: 4x + -5x = -1x (-20 + -1x + x2) = 180 Solving -20 + -1x + x2 = 180 Solving for variable 'x'. Reorder the terms: -20 + -180 + -1x + x2 = 180 + -180 Combine like terms: -20 + -180 = -200 -200 + -1x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -200 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + -1x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -1x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -1x + x2 = 0 + 200 -1x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -1x + x2 = 200 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 200 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 200 + 0.25 Combine like terms: 200 + 0.25 = 200.25 0.25 + -1x + x2 = 200.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + -0.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + -0.5 = 14.150971698 Simplifying x + -0.5 = 14.150971698 Reorder the terms: -0.5 + x = 14.150971698 Solving -0.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 14.150971698 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 14.150971698 + 0.5 x = 14.150971698 + 0.5 Combine like terms: 14.150971698 + 0.5 = 14.650971698 x = 14.650971698 Simplifying x = 14.650971698Subproblem 2
x + -0.5 = -14.150971698 Simplifying x + -0.5 = -14.150971698 Reorder the terms: -0.5 + x = -14.150971698 Solving -0.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -14.150971698 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -14.150971698 + 0.5 x = -14.150971698 + 0.5 Combine like terms: -14.150971698 + 0.5 = -13.650971698 x = -13.650971698 Simplifying x = -13.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.650971698, -13.650971698}
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