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Simplifying 17x2 + 61x + 40 = 0 Reorder the terms: 40 + 61x + 17x2 = 0 Solving 40 + 61x + 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'. 2.352941176 + 3.588235294x + x2 = 0 Move the constant term to the right: Add '-2.352941176' to each side of the equation. 2.352941176 + 3.588235294x + -2.352941176 + x2 = 0 + -2.352941176 Reorder the terms: 2.352941176 + -2.352941176 + 3.588235294x + x2 = 0 + -2.352941176 Combine like terms: 2.352941176 + -2.352941176 = 0.000000000 0.000000000 + 3.588235294x + x2 = 0 + -2.352941176 3.588235294x + x2 = 0 + -2.352941176 Combine like terms: 0 + -2.352941176 = -2.352941176 3.588235294x + x2 = -2.352941176 The x term is 3.588235294x. Take half its coefficient (1.794117647). Square it (3.218858131) and add it to both sides. Add '3.218858131' to each side of the equation. 3.588235294x + 3.218858131 + x2 = -2.352941176 + 3.218858131 Reorder the terms: 3.218858131 + 3.588235294x + x2 = -2.352941176 + 3.218858131 Combine like terms: -2.352941176 + 3.218858131 = 0.865916955 3.218858131 + 3.588235294x + x2 = 0.865916955 Factor a perfect square on the left side: (x + 1.794117647)(x + 1.794117647) = 0.865916955 Calculate the square root of the right side: 0.930546589 Break this problem into two subproblems by setting (x + 1.794117647) equal to 0.930546589 and -0.930546589.Subproblem 1
x + 1.794117647 = 0.930546589 Simplifying x + 1.794117647 = 0.930546589 Reorder the terms: 1.794117647 + x = 0.930546589 Solving 1.794117647 + x = 0.930546589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.794117647' to each side of the equation. 1.794117647 + -1.794117647 + x = 0.930546589 + -1.794117647 Combine like terms: 1.794117647 + -1.794117647 = 0.000000000 0.000000000 + x = 0.930546589 + -1.794117647 x = 0.930546589 + -1.794117647 Combine like terms: 0.930546589 + -1.794117647 = -0.863571058 x = -0.863571058 Simplifying x = -0.863571058Subproblem 2
x + 1.794117647 = -0.930546589 Simplifying x + 1.794117647 = -0.930546589 Reorder the terms: 1.794117647 + x = -0.930546589 Solving 1.794117647 + x = -0.930546589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.794117647' to each side of the equation. 1.794117647 + -1.794117647 + x = -0.930546589 + -1.794117647 Combine like terms: 1.794117647 + -1.794117647 = 0.000000000 0.000000000 + x = -0.930546589 + -1.794117647 x = -0.930546589 + -1.794117647 Combine like terms: -0.930546589 + -1.794117647 = -2.724664236 x = -2.724664236 Simplifying x = -2.724664236Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.863571058, -2.724664236}
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