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Simplifying 17x2 + -46x + 14 = 81 Reorder the terms: 14 + -46x + 17x2 = 81 Solving 14 + -46x + 17x2 = 81 Solving for variable 'x'. Reorder the terms: 14 + -81 + -46x + 17x2 = 81 + -81 Combine like terms: 14 + -81 = -67 -67 + -46x + 17x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -67 + -46x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -3.941176471 + -2.705882353x + x2 = 0 Move the constant term to the right: Add '3.941176471' to each side of the equation. -3.941176471 + -2.705882353x + 3.941176471 + x2 = 0 + 3.941176471 Reorder the terms: -3.941176471 + 3.941176471 + -2.705882353x + x2 = 0 + 3.941176471 Combine like terms: -3.941176471 + 3.941176471 = 0.000000000 0.000000000 + -2.705882353x + x2 = 0 + 3.941176471 -2.705882353x + x2 = 0 + 3.941176471 Combine like terms: 0 + 3.941176471 = 3.941176471 -2.705882353x + x2 = 3.941176471 The x term is -2.705882353x. Take half its coefficient (-1.352941177). Square it (1.830449828) and add it to both sides. Add '1.830449828' to each side of the equation. -2.705882353x + 1.830449828 + x2 = 3.941176471 + 1.830449828 Reorder the terms: 1.830449828 + -2.705882353x + x2 = 3.941176471 + 1.830449828 Combine like terms: 3.941176471 + 1.830449828 = 5.771626299 1.830449828 + -2.705882353x + x2 = 5.771626299 Factor a perfect square on the left side: (x + -1.352941177)(x + -1.352941177) = 5.771626299 Calculate the square root of the right side: 2.402420925 Break this problem into two subproblems by setting (x + -1.352941177) equal to 2.402420925 and -2.402420925.Subproblem 1
x + -1.352941177 = 2.402420925 Simplifying x + -1.352941177 = 2.402420925 Reorder the terms: -1.352941177 + x = 2.402420925 Solving -1.352941177 + x = 2.402420925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.352941177' to each side of the equation. -1.352941177 + 1.352941177 + x = 2.402420925 + 1.352941177 Combine like terms: -1.352941177 + 1.352941177 = 0.000000000 0.000000000 + x = 2.402420925 + 1.352941177 x = 2.402420925 + 1.352941177 Combine like terms: 2.402420925 + 1.352941177 = 3.755362102 x = 3.755362102 Simplifying x = 3.755362102Subproblem 2
x + -1.352941177 = -2.402420925 Simplifying x + -1.352941177 = -2.402420925 Reorder the terms: -1.352941177 + x = -2.402420925 Solving -1.352941177 + x = -2.402420925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.352941177' to each side of the equation. -1.352941177 + 1.352941177 + x = -2.402420925 + 1.352941177 Combine like terms: -1.352941177 + 1.352941177 = 0.000000000 0.000000000 + x = -2.402420925 + 1.352941177 x = -2.402420925 + 1.352941177 Combine like terms: -2.402420925 + 1.352941177 = -1.049479748 x = -1.049479748 Simplifying x = -1.049479748Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.755362102, -1.049479748}
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