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Simplifying 8x2 + -17x + -671 = 0 Reorder the terms: -671 + -17x + 8x2 = 0 Solving -671 + -17x + 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'. -83.875 + -2.125x + x2 = 0 Move the constant term to the right: Add '83.875' to each side of the equation. -83.875 + -2.125x + 83.875 + x2 = 0 + 83.875 Reorder the terms: -83.875 + 83.875 + -2.125x + x2 = 0 + 83.875 Combine like terms: -83.875 + 83.875 = 0.000 0.000 + -2.125x + x2 = 0 + 83.875 -2.125x + x2 = 0 + 83.875 Combine like terms: 0 + 83.875 = 83.875 -2.125x + x2 = 83.875 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = 83.875 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 83.875 + 1.12890625 Combine like terms: 83.875 + 1.12890625 = 85.00390625 1.12890625 + -2.125x + x2 = 85.00390625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 85.00390625 Calculate the square root of the right side: 9.219756301 Break this problem into two subproblems by setting (x + -1.0625) equal to 9.219756301 and -9.219756301.Subproblem 1
x + -1.0625 = 9.219756301 Simplifying x + -1.0625 = 9.219756301 Reorder the terms: -1.0625 + x = 9.219756301 Solving -1.0625 + x = 9.219756301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 9.219756301 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 9.219756301 + 1.0625 x = 9.219756301 + 1.0625 Combine like terms: 9.219756301 + 1.0625 = 10.282256301 x = 10.282256301 Simplifying x = 10.282256301Subproblem 2
x + -1.0625 = -9.219756301 Simplifying x + -1.0625 = -9.219756301 Reorder the terms: -1.0625 + x = -9.219756301 Solving -1.0625 + x = -9.219756301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -9.219756301 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -9.219756301 + 1.0625 x = -9.219756301 + 1.0625 Combine like terms: -9.219756301 + 1.0625 = -8.157256301 x = -8.157256301 Simplifying x = -8.157256301Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.282256301, -8.157256301}
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