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Simplifying 17x2 + -8x + -234 = 0 Reorder the terms: -234 + -8x + 17x2 = 0 Solving -234 + -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'. -13.76470588 + -0.4705882353x + x2 = 0 Move the constant term to the right: Add '13.76470588' to each side of the equation. -13.76470588 + -0.4705882353x + 13.76470588 + x2 = 0 + 13.76470588 Reorder the terms: -13.76470588 + 13.76470588 + -0.4705882353x + x2 = 0 + 13.76470588 Combine like terms: -13.76470588 + 13.76470588 = 0.00000000 0.00000000 + -0.4705882353x + x2 = 0 + 13.76470588 -0.4705882353x + x2 = 0 + 13.76470588 Combine like terms: 0 + 13.76470588 = 13.76470588 -0.4705882353x + x2 = 13.76470588 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 = 13.76470588 + 0.05536332182 Reorder the terms: 0.05536332182 + -0.4705882353x + x2 = 13.76470588 + 0.05536332182 Combine like terms: 13.76470588 + 0.05536332182 = 13.82006920182 0.05536332182 + -0.4705882353x + x2 = 13.82006920182 Factor a perfect square on the left side: (x + -0.2352941177)(x + -0.2352941177) = 13.82006920182 Calculate the square root of the right side: 3.717535367 Break this problem into two subproblems by setting (x + -0.2352941177) equal to 3.717535367 and -3.717535367.Subproblem 1
x + -0.2352941177 = 3.717535367 Simplifying x + -0.2352941177 = 3.717535367 Reorder the terms: -0.2352941177 + x = 3.717535367 Solving -0.2352941177 + x = 3.717535367 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 = 3.717535367 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = 3.717535367 + 0.2352941177 x = 3.717535367 + 0.2352941177 Combine like terms: 3.717535367 + 0.2352941177 = 3.9528294847 x = 3.9528294847 Simplifying x = 3.9528294847Subproblem 2
x + -0.2352941177 = -3.717535367 Simplifying x + -0.2352941177 = -3.717535367 Reorder the terms: -0.2352941177 + x = -3.717535367 Solving -0.2352941177 + x = -3.717535367 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 = -3.717535367 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = -3.717535367 + 0.2352941177 x = -3.717535367 + 0.2352941177 Combine like terms: -3.717535367 + 0.2352941177 = -3.4822412493 x = -3.4822412493 Simplifying x = -3.4822412493Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9528294847, -3.4822412493}
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