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Simplifying 8x2 + -441x + 60 = 0 Reorder the terms: 60 + -441x + 8x2 = 0 Solving 60 + -441x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 7.5 + -55.125x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -55.125x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -55.125x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -55.125x + x2 = 0 + -7.5 -55.125x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -55.125x + x2 = -7.5 The x term is -55.125x. Take half its coefficient (-27.5625). Square it (759.6914063) and add it to both sides. Add '759.6914063' to each side of the equation. -55.125x + 759.6914063 + x2 = -7.5 + 759.6914063 Reorder the terms: 759.6914063 + -55.125x + x2 = -7.5 + 759.6914063 Combine like terms: -7.5 + 759.6914063 = 752.1914063 759.6914063 + -55.125x + x2 = 752.1914063 Factor a perfect square on the left side: (x + -27.5625)(x + -27.5625) = 752.1914063 Calculate the square root of the right side: 27.426108114 Break this problem into two subproblems by setting (x + -27.5625) equal to 27.426108114 and -27.426108114.Subproblem 1
x + -27.5625 = 27.426108114 Simplifying x + -27.5625 = 27.426108114 Reorder the terms: -27.5625 + x = 27.426108114 Solving -27.5625 + x = 27.426108114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5625' to each side of the equation. -27.5625 + 27.5625 + x = 27.426108114 + 27.5625 Combine like terms: -27.5625 + 27.5625 = 0.0000 0.0000 + x = 27.426108114 + 27.5625 x = 27.426108114 + 27.5625 Combine like terms: 27.426108114 + 27.5625 = 54.988608114 x = 54.988608114 Simplifying x = 54.988608114Subproblem 2
x + -27.5625 = -27.426108114 Simplifying x + -27.5625 = -27.426108114 Reorder the terms: -27.5625 + x = -27.426108114 Solving -27.5625 + x = -27.426108114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5625' to each side of the equation. -27.5625 + 27.5625 + x = -27.426108114 + 27.5625 Combine like terms: -27.5625 + 27.5625 = 0.0000 0.0000 + x = -27.426108114 + 27.5625 x = -27.426108114 + 27.5625 Combine like terms: -27.426108114 + 27.5625 = 0.136391886 x = 0.136391886 Simplifying x = 0.136391886Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.988608114, 0.136391886}
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