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Simplifying 7x2 + -92x + -9 = 0 Reorder the terms: -9 + -92x + 7x2 = 0 Solving -9 + -92x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + -13.14285714x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -13.14285714x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -13.14285714x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -13.14285714x + x2 = 0 + 1.285714286 -13.14285714x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -13.14285714x + x2 = 1.285714286 The x term is -13.14285714x. Take half its coefficient (-6.57142857). Square it (43.18367345) and add it to both sides. Add '43.18367345' to each side of the equation. -13.14285714x + 43.18367345 + x2 = 1.285714286 + 43.18367345 Reorder the terms: 43.18367345 + -13.14285714x + x2 = 1.285714286 + 43.18367345 Combine like terms: 1.285714286 + 43.18367345 = 44.469387736 43.18367345 + -13.14285714x + x2 = 44.469387736 Factor a perfect square on the left side: (x + -6.57142857)(x + -6.57142857) = 44.469387736 Calculate the square root of the right side: 6.668537151 Break this problem into two subproblems by setting (x + -6.57142857) equal to 6.668537151 and -6.668537151.Subproblem 1
x + -6.57142857 = 6.668537151 Simplifying x + -6.57142857 = 6.668537151 Reorder the terms: -6.57142857 + x = 6.668537151 Solving -6.57142857 + x = 6.668537151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.57142857' to each side of the equation. -6.57142857 + 6.57142857 + x = 6.668537151 + 6.57142857 Combine like terms: -6.57142857 + 6.57142857 = 0.00000000 0.00000000 + x = 6.668537151 + 6.57142857 x = 6.668537151 + 6.57142857 Combine like terms: 6.668537151 + 6.57142857 = 13.239965721 x = 13.239965721 Simplifying x = 13.239965721Subproblem 2
x + -6.57142857 = -6.668537151 Simplifying x + -6.57142857 = -6.668537151 Reorder the terms: -6.57142857 + x = -6.668537151 Solving -6.57142857 + x = -6.668537151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.57142857' to each side of the equation. -6.57142857 + 6.57142857 + x = -6.668537151 + 6.57142857 Combine like terms: -6.57142857 + 6.57142857 = 0.00000000 0.00000000 + x = -6.668537151 + 6.57142857 x = -6.668537151 + 6.57142857 Combine like terms: -6.668537151 + 6.57142857 = -0.097108581 x = -0.097108581 Simplifying x = -0.097108581Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.239965721, -0.097108581}
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