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Simplifying 8x2 + -10x + -97 = 0 Reorder the terms: -97 + -10x + 8x2 = 0 Solving -97 + -10x + 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'. -12.125 + -1.25x + x2 = 0 Move the constant term to the right: Add '12.125' to each side of the equation. -12.125 + -1.25x + 12.125 + x2 = 0 + 12.125 Reorder the terms: -12.125 + 12.125 + -1.25x + x2 = 0 + 12.125 Combine like terms: -12.125 + 12.125 = 0.000 0.000 + -1.25x + x2 = 0 + 12.125 -1.25x + x2 = 0 + 12.125 Combine like terms: 0 + 12.125 = 12.125 -1.25x + x2 = 12.125 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 12.125 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 12.125 + 0.390625 Combine like terms: 12.125 + 0.390625 = 12.515625 0.390625 + -1.25x + x2 = 12.515625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 12.515625 Calculate the square root of the right side: 3.537742925 Break this problem into two subproblems by setting (x + -0.625) equal to 3.537742925 and -3.537742925.Subproblem 1
x + -0.625 = 3.537742925 Simplifying x + -0.625 = 3.537742925 Reorder the terms: -0.625 + x = 3.537742925 Solving -0.625 + x = 3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 3.537742925 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 3.537742925 + 0.625 x = 3.537742925 + 0.625 Combine like terms: 3.537742925 + 0.625 = 4.162742925 x = 4.162742925 Simplifying x = 4.162742925Subproblem 2
x + -0.625 = -3.537742925 Simplifying x + -0.625 = -3.537742925 Reorder the terms: -0.625 + x = -3.537742925 Solving -0.625 + x = -3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -3.537742925 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -3.537742925 + 0.625 x = -3.537742925 + 0.625 Combine like terms: -3.537742925 + 0.625 = -2.912742925 x = -2.912742925 Simplifying x = -2.912742925Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.162742925, -2.912742925}
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