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Simplifying x2 + -22.5x = 88 Reorder the terms: -22.5x + x2 = 88 Solving -22.5x + x2 = 88 Solving for variable 'x'. Reorder the terms: -88 + -22.5x + x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + -22.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -22.5x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + -22.5x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -22.5x + x2 = 0 + 88 -22.5x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 -22.5x + x2 = 88 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = 88 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 88 + 126.5625 Combine like terms: 88 + 126.5625 = 214.5625 126.5625 + -22.5x + x2 = 214.5625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 214.5625 Calculate the square root of the right side: 14.647952075 Break this problem into two subproblems by setting (x + -11.25) equal to 14.647952075 and -14.647952075.Subproblem 1
x + -11.25 = 14.647952075 Simplifying x + -11.25 = 14.647952075 Reorder the terms: -11.25 + x = 14.647952075 Solving -11.25 + x = 14.647952075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 14.647952075 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 14.647952075 + 11.25 x = 14.647952075 + 11.25 Combine like terms: 14.647952075 + 11.25 = 25.897952075 x = 25.897952075 Simplifying x = 25.897952075Subproblem 2
x + -11.25 = -14.647952075 Simplifying x + -11.25 = -14.647952075 Reorder the terms: -11.25 + x = -14.647952075 Solving -11.25 + x = -14.647952075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -14.647952075 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -14.647952075 + 11.25 x = -14.647952075 + 11.25 Combine like terms: -14.647952075 + 11.25 = -3.397952075 x = -3.397952075 Simplifying x = -3.397952075Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.897952075, -3.397952075}
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