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Simplifying -0.57x2 + 30.48x + 119.85 = 238 Reorder the terms: 119.85 + 30.48x + -0.57x2 = 238 Solving 119.85 + 30.48x + -0.57x2 = 238 Solving for variable 'x'. Reorder the terms: 119.85 + -238 + 30.48x + -0.57x2 = 238 + -238 Combine like terms: 119.85 + -238 = -118.15 -118.15 + 30.48x + -0.57x2 = 238 + -238 Combine like terms: 238 + -238 = 0 -118.15 + 30.48x + -0.57x2 = 0 Begin completing the square. Divide all terms by -0.57 the coefficient of the squared term: Divide each side by '-0.57'. 207.2807018 + -53.47368421x + x2 = 0 Move the constant term to the right: Add '-207.2807018' to each side of the equation. 207.2807018 + -53.47368421x + -207.2807018 + x2 = 0 + -207.2807018 Reorder the terms: 207.2807018 + -207.2807018 + -53.47368421x + x2 = 0 + -207.2807018 Combine like terms: 207.2807018 + -207.2807018 = 0.0000000 0.0000000 + -53.47368421x + x2 = 0 + -207.2807018 -53.47368421x + x2 = 0 + -207.2807018 Combine like terms: 0 + -207.2807018 = -207.2807018 -53.47368421x + x2 = -207.2807018 The x term is -53.47368421x. Take half its coefficient (-26.73684211). Square it (714.8587260) and add it to both sides. Add '714.8587260' to each side of the equation. -53.47368421x + 714.8587260 + x2 = -207.2807018 + 714.8587260 Reorder the terms: 714.8587260 + -53.47368421x + x2 = -207.2807018 + 714.8587260 Combine like terms: -207.2807018 + 714.8587260 = 507.5780242 714.8587260 + -53.47368421x + x2 = 507.5780242 Factor a perfect square on the left side: (x + -26.73684211)(x + -26.73684211) = 507.5780242 Calculate the square root of the right side: 22.52949232 Break this problem into two subproblems by setting (x + -26.73684211) equal to 22.52949232 and -22.52949232.Subproblem 1
x + -26.73684211 = 22.52949232 Simplifying x + -26.73684211 = 22.52949232 Reorder the terms: -26.73684211 + x = 22.52949232 Solving -26.73684211 + x = 22.52949232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.73684211' to each side of the equation. -26.73684211 + 26.73684211 + x = 22.52949232 + 26.73684211 Combine like terms: -26.73684211 + 26.73684211 = 0.00000000 0.00000000 + x = 22.52949232 + 26.73684211 x = 22.52949232 + 26.73684211 Combine like terms: 22.52949232 + 26.73684211 = 49.26633443 x = 49.26633443 Simplifying x = 49.26633443Subproblem 2
x + -26.73684211 = -22.52949232 Simplifying x + -26.73684211 = -22.52949232 Reorder the terms: -26.73684211 + x = -22.52949232 Solving -26.73684211 + x = -22.52949232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.73684211' to each side of the equation. -26.73684211 + 26.73684211 + x = -22.52949232 + 26.73684211 Combine like terms: -26.73684211 + 26.73684211 = 0.00000000 0.00000000 + x = -22.52949232 + 26.73684211 x = -22.52949232 + 26.73684211 Combine like terms: -22.52949232 + 26.73684211 = 4.20734979 x = 4.20734979 Simplifying x = 4.20734979Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.26633443, 4.20734979}
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