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Simplifying 36x + -0.8x2 = 202.5 Solving 36x + -0.8x2 = 202.5 Solving for variable 'x'. Reorder the terms: -202.5 + 36x + -0.8x2 = 202.5 + -202.5 Combine like terms: 202.5 + -202.5 = 0.0 -202.5 + 36x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 253.125 + -45x + x2 = 0 Move the constant term to the right: Add '-253.125' to each side of the equation. 253.125 + -45x + -253.125 + x2 = 0 + -253.125 Reorder the terms: 253.125 + -253.125 + -45x + x2 = 0 + -253.125 Combine like terms: 253.125 + -253.125 = 0.000 0.000 + -45x + x2 = 0 + -253.125 -45x + x2 = 0 + -253.125 Combine like terms: 0 + -253.125 = -253.125 -45x + x2 = -253.125 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -253.125 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -253.125 + 506.25 Combine like terms: -253.125 + 506.25 = 253.125 506.25 + -45x + x2 = 253.125 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 253.125 Calculate the square root of the right side: 15.909902577 Break this problem into two subproblems by setting (x + -22.5) equal to 15.909902577 and -15.909902577.Subproblem 1
x + -22.5 = 15.909902577 Simplifying x + -22.5 = 15.909902577 Reorder the terms: -22.5 + x = 15.909902577 Solving -22.5 + x = 15.909902577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 15.909902577 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 15.909902577 + 22.5 x = 15.909902577 + 22.5 Combine like terms: 15.909902577 + 22.5 = 38.409902577 x = 38.409902577 Simplifying x = 38.409902577Subproblem 2
x + -22.5 = -15.909902577 Simplifying x + -22.5 = -15.909902577 Reorder the terms: -22.5 + x = -15.909902577 Solving -22.5 + x = -15.909902577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -15.909902577 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -15.909902577 + 22.5 x = -15.909902577 + 22.5 Combine like terms: -15.909902577 + 22.5 = 6.590097423 x = 6.590097423 Simplifying x = 6.590097423Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.409902577, 6.590097423}
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