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Simplifying -17x2 + -27x + 4 = 0 Reorder the terms: 4 + -27x + -17x2 = 0 Solving 4 + -27x + -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 + 1.588235294x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + 1.588235294x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + 1.588235294x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + 1.588235294x + x2 = 0 + 0.2352941176 1.588235294x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 1.588235294x + x2 = 0.2352941176 The x term is 1.588235294x. Take half its coefficient (0.794117647). Square it (0.6306228373) and add it to both sides. Add '0.6306228373' to each side of the equation. 1.588235294x + 0.6306228373 + x2 = 0.2352941176 + 0.6306228373 Reorder the terms: 0.6306228373 + 1.588235294x + x2 = 0.2352941176 + 0.6306228373 Combine like terms: 0.2352941176 + 0.6306228373 = 0.8659169549 0.6306228373 + 1.588235294x + x2 = 0.8659169549 Factor a perfect square on the left side: (x + 0.794117647)(x + 0.794117647) = 0.8659169549 Calculate the square root of the right side: 0.930546589 Break this problem into two subproblems by setting (x + 0.794117647) equal to 0.930546589 and -0.930546589.Subproblem 1
x + 0.794117647 = 0.930546589 Simplifying x + 0.794117647 = 0.930546589 Reorder the terms: 0.794117647 + x = 0.930546589 Solving 0.794117647 + x = 0.930546589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.794117647' to each side of the equation. 0.794117647 + -0.794117647 + x = 0.930546589 + -0.794117647 Combine like terms: 0.794117647 + -0.794117647 = 0.000000000 0.000000000 + x = 0.930546589 + -0.794117647 x = 0.930546589 + -0.794117647 Combine like terms: 0.930546589 + -0.794117647 = 0.136428942 x = 0.136428942 Simplifying x = 0.136428942Subproblem 2
x + 0.794117647 = -0.930546589 Simplifying x + 0.794117647 = -0.930546589 Reorder the terms: 0.794117647 + x = -0.930546589 Solving 0.794117647 + x = -0.930546589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.794117647' to each side of the equation. 0.794117647 + -0.794117647 + x = -0.930546589 + -0.794117647 Combine like terms: 0.794117647 + -0.794117647 = 0.000000000 0.000000000 + x = -0.930546589 + -0.794117647 x = -0.930546589 + -0.794117647 Combine like terms: -0.930546589 + -0.794117647 = -1.724664236 x = -1.724664236 Simplifying x = -1.724664236Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.136428942, -1.724664236}
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