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Simplifying 17x2 + -8x + -4 = 0 Reorder the terms: -4 + -8x + 17x2 = 0 Solving -4 + -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'. -0.2352941176 + -0.4705882353x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + -0.4705882353x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + -0.4705882353x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + -0.4705882353x + x2 = 0 + 0.2352941176 -0.4705882353x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 -0.4705882353x + x2 = 0.2352941176 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 = 0.2352941176 + 0.05536332182 Reorder the terms: 0.05536332182 + -0.4705882353x + x2 = 0.2352941176 + 0.05536332182 Combine like terms: 0.2352941176 + 0.05536332182 = 0.29065743942 0.05536332182 + -0.4705882353x + x2 = 0.29065743942 Factor a perfect square on the left side: (x + -0.2352941177)(x + -0.2352941177) = 0.29065743942 Calculate the square root of the right side: 0.539126552 Break this problem into two subproblems by setting (x + -0.2352941177) equal to 0.539126552 and -0.539126552.Subproblem 1
x + -0.2352941177 = 0.539126552 Simplifying x + -0.2352941177 = 0.539126552 Reorder the terms: -0.2352941177 + x = 0.539126552 Solving -0.2352941177 + x = 0.539126552 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 = 0.539126552 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = 0.539126552 + 0.2352941177 x = 0.539126552 + 0.2352941177 Combine like terms: 0.539126552 + 0.2352941177 = 0.7744206697 x = 0.7744206697 Simplifying x = 0.7744206697Subproblem 2
x + -0.2352941177 = -0.539126552 Simplifying x + -0.2352941177 = -0.539126552 Reorder the terms: -0.2352941177 + x = -0.539126552 Solving -0.2352941177 + x = -0.539126552 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 = -0.539126552 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = -0.539126552 + 0.2352941177 x = -0.539126552 + 0.2352941177 Combine like terms: -0.539126552 + 0.2352941177 = -0.3038324343 x = -0.3038324343 Simplifying x = -0.3038324343Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7744206697, -0.3038324343}
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