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Simplifying 17x2 + -8x + -2 = 0 Reorder the terms: -2 + -8x + 17x2 = 0 Solving -2 + -8x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.1176470588 + -0.4705882353x + x2 = 0 Move the constant term to the right: Add '0.1176470588' to each side of the equation. -0.1176470588 + -0.4705882353x + 0.1176470588 + x2 = 0 + 0.1176470588 Reorder the terms: -0.1176470588 + 0.1176470588 + -0.4705882353x + x2 = 0 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + -0.4705882353x + x2 = 0 + 0.1176470588 -0.4705882353x + x2 = 0 + 0.1176470588 Combine like terms: 0 + 0.1176470588 = 0.1176470588 -0.4705882353x + x2 = 0.1176470588 The x term is -0.4705882353x. Take half its coefficient (-0.2352941177). Square it (0.05536332182) and add it to both sides. Add '0.05536332182' to each side of the equation. -0.4705882353x + 0.05536332182 + x2 = 0.1176470588 + 0.05536332182 Reorder the terms: 0.05536332182 + -0.4705882353x + x2 = 0.1176470588 + 0.05536332182 Combine like terms: 0.1176470588 + 0.05536332182 = 0.17301038062 0.05536332182 + -0.4705882353x + x2 = 0.17301038062 Factor a perfect square on the left side: (x + -0.2352941177)(x + -0.2352941177) = 0.17301038062 Calculate the square root of the right side: 0.415945165 Break this problem into two subproblems by setting (x + -0.2352941177) equal to 0.415945165 and -0.415945165.Subproblem 1
x + -0.2352941177 = 0.415945165 Simplifying x + -0.2352941177 = 0.415945165 Reorder the terms: -0.2352941177 + x = 0.415945165 Solving -0.2352941177 + x = 0.415945165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2352941177' to each side of the equation. -0.2352941177 + 0.2352941177 + x = 0.415945165 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = 0.415945165 + 0.2352941177 x = 0.415945165 + 0.2352941177 Combine like terms: 0.415945165 + 0.2352941177 = 0.6512392827 x = 0.6512392827 Simplifying x = 0.6512392827Subproblem 2
x + -0.2352941177 = -0.415945165 Simplifying x + -0.2352941177 = -0.415945165 Reorder the terms: -0.2352941177 + x = -0.415945165 Solving -0.2352941177 + x = -0.415945165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2352941177' to each side of the equation. -0.2352941177 + 0.2352941177 + x = -0.415945165 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = -0.415945165 + 0.2352941177 x = -0.415945165 + 0.2352941177 Combine like terms: -0.415945165 + 0.2352941177 = -0.1806510473 x = -0.1806510473 Simplifying x = -0.1806510473Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6512392827, -0.1806510473}
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