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Simplifying 60x + -2x2 = 22x + 91 Reorder the terms: 60x + -2x2 = 91 + 22x Solving 60x + -2x2 = 91 + 22x Solving for variable 'x'. Reorder the terms: -91 + 60x + -22x + -2x2 = 91 + 22x + -91 + -22x Combine like terms: 60x + -22x = 38x -91 + 38x + -2x2 = 91 + 22x + -91 + -22x Reorder the terms: -91 + 38x + -2x2 = 91 + -91 + 22x + -22x Combine like terms: 91 + -91 = 0 -91 + 38x + -2x2 = 0 + 22x + -22x -91 + 38x + -2x2 = 22x + -22x Combine like terms: 22x + -22x = 0 -91 + 38x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 45.5 + -19x + x2 = 0 Move the constant term to the right: Add '-45.5' to each side of the equation. 45.5 + -19x + -45.5 + x2 = 0 + -45.5 Reorder the terms: 45.5 + -45.5 + -19x + x2 = 0 + -45.5 Combine like terms: 45.5 + -45.5 = 0.0 0.0 + -19x + x2 = 0 + -45.5 -19x + x2 = 0 + -45.5 Combine like terms: 0 + -45.5 = -45.5 -19x + x2 = -45.5 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -45.5 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -45.5 + 90.25 Combine like terms: -45.5 + 90.25 = 44.75 90.25 + -19x + x2 = 44.75 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 44.75 Calculate the square root of the right side: 6.68954408 Break this problem into two subproblems by setting (x + -9.5) equal to 6.68954408 and -6.68954408.Subproblem 1
x + -9.5 = 6.68954408 Simplifying x + -9.5 = 6.68954408 Reorder the terms: -9.5 + x = 6.68954408 Solving -9.5 + x = 6.68954408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 6.68954408 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 6.68954408 + 9.5 x = 6.68954408 + 9.5 Combine like terms: 6.68954408 + 9.5 = 16.18954408 x = 16.18954408 Simplifying x = 16.18954408Subproblem 2
x + -9.5 = -6.68954408 Simplifying x + -9.5 = -6.68954408 Reorder the terms: -9.5 + x = -6.68954408 Solving -9.5 + x = -6.68954408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -6.68954408 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -6.68954408 + 9.5 x = -6.68954408 + 9.5 Combine like terms: -6.68954408 + 9.5 = 2.81045592 x = 2.81045592 Simplifying x = 2.81045592Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.18954408, 2.81045592}
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