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Simplifying 7x2 + -174x + -9 = 0 Reorder the terms: -9 + -174x + 7x2 = 0 Solving -9 + -174x + 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 + -24.85714286x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -24.85714286x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -24.85714286x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -24.85714286x + x2 = 0 + 1.285714286 -24.85714286x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -24.85714286x + x2 = 1.285714286 The x term is -24.85714286x. Take half its coefficient (-12.42857143). Square it (154.4693878) and add it to both sides. Add '154.4693878' to each side of the equation. -24.85714286x + 154.4693878 + x2 = 1.285714286 + 154.4693878 Reorder the terms: 154.4693878 + -24.85714286x + x2 = 1.285714286 + 154.4693878 Combine like terms: 1.285714286 + 154.4693878 = 155.755102086 154.4693878 + -24.85714286x + x2 = 155.755102086 Factor a perfect square on the left side: (x + -12.42857143)(x + -12.42857143) = 155.755102086 Calculate the square root of the right side: 12.480188383 Break this problem into two subproblems by setting (x + -12.42857143) equal to 12.480188383 and -12.480188383.Subproblem 1
x + -12.42857143 = 12.480188383 Simplifying x + -12.42857143 = 12.480188383 Reorder the terms: -12.42857143 + x = 12.480188383 Solving -12.42857143 + x = 12.480188383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.42857143' to each side of the equation. -12.42857143 + 12.42857143 + x = 12.480188383 + 12.42857143 Combine like terms: -12.42857143 + 12.42857143 = 0.00000000 0.00000000 + x = 12.480188383 + 12.42857143 x = 12.480188383 + 12.42857143 Combine like terms: 12.480188383 + 12.42857143 = 24.908759813 x = 24.908759813 Simplifying x = 24.908759813Subproblem 2
x + -12.42857143 = -12.480188383 Simplifying x + -12.42857143 = -12.480188383 Reorder the terms: -12.42857143 + x = -12.480188383 Solving -12.42857143 + x = -12.480188383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.42857143' to each side of the equation. -12.42857143 + 12.42857143 + x = -12.480188383 + 12.42857143 Combine like terms: -12.42857143 + 12.42857143 = 0.00000000 0.00000000 + x = -12.480188383 + 12.42857143 x = -12.480188383 + 12.42857143 Combine like terms: -12.480188383 + 12.42857143 = -0.051616953 x = -0.051616953 Simplifying x = -0.051616953Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.908759813, -0.051616953}
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