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Simplifying 17x2 + 16x + -32 = 0 Reorder the terms: -32 + 16x + 17x2 = 0 Solving -32 + 16x + 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'. -1.882352941 + 0.9411764706x + x2 = 0 Move the constant term to the right: Add '1.882352941' to each side of the equation. -1.882352941 + 0.9411764706x + 1.882352941 + x2 = 0 + 1.882352941 Reorder the terms: -1.882352941 + 1.882352941 + 0.9411764706x + x2 = 0 + 1.882352941 Combine like terms: -1.882352941 + 1.882352941 = 0.000000000 0.000000000 + 0.9411764706x + x2 = 0 + 1.882352941 0.9411764706x + x2 = 0 + 1.882352941 Combine like terms: 0 + 1.882352941 = 1.882352941 0.9411764706x + x2 = 1.882352941 The x term is 0.9411764706x. Take half its coefficient (0.4705882353). Square it (0.2214532872) and add it to both sides. Add '0.2214532872' to each side of the equation. 0.9411764706x + 0.2214532872 + x2 = 1.882352941 + 0.2214532872 Reorder the terms: 0.2214532872 + 0.9411764706x + x2 = 1.882352941 + 0.2214532872 Combine like terms: 1.882352941 + 0.2214532872 = 2.1038062282 0.2214532872 + 0.9411764706x + x2 = 2.1038062282 Factor a perfect square on the left side: (x + 0.4705882353)(x + 0.4705882353) = 2.1038062282 Calculate the square root of the right side: 1.450450354 Break this problem into two subproblems by setting (x + 0.4705882353) equal to 1.450450354 and -1.450450354.Subproblem 1
x + 0.4705882353 = 1.450450354 Simplifying x + 0.4705882353 = 1.450450354 Reorder the terms: 0.4705882353 + x = 1.450450354 Solving 0.4705882353 + x = 1.450450354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4705882353' to each side of the equation. 0.4705882353 + -0.4705882353 + x = 1.450450354 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + x = 1.450450354 + -0.4705882353 x = 1.450450354 + -0.4705882353 Combine like terms: 1.450450354 + -0.4705882353 = 0.9798621187 x = 0.9798621187 Simplifying x = 0.9798621187Subproblem 2
x + 0.4705882353 = -1.450450354 Simplifying x + 0.4705882353 = -1.450450354 Reorder the terms: 0.4705882353 + x = -1.450450354 Solving 0.4705882353 + x = -1.450450354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4705882353' to each side of the equation. 0.4705882353 + -0.4705882353 + x = -1.450450354 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + x = -1.450450354 + -0.4705882353 x = -1.450450354 + -0.4705882353 Combine like terms: -1.450450354 + -0.4705882353 = -1.9210385893 x = -1.9210385893 Simplifying x = -1.9210385893Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9798621187, -1.9210385893}
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