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Simplifying 17x2 + -24x + 8 = 0 Reorder the terms: 8 + -24x + 17x2 = 0 Solving 8 + -24x + 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'. 0.4705882353 + -1.411764706x + x2 = 0 Move the constant term to the right: Add '-0.4705882353' to each side of the equation. 0.4705882353 + -1.411764706x + -0.4705882353 + x2 = 0 + -0.4705882353 Reorder the terms: 0.4705882353 + -0.4705882353 + -1.411764706x + x2 = 0 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + -1.411764706x + x2 = 0 + -0.4705882353 -1.411764706x + x2 = 0 + -0.4705882353 Combine like terms: 0 + -0.4705882353 = -0.4705882353 -1.411764706x + x2 = -0.4705882353 The x term is -1.411764706x. Take half its coefficient (-0.705882353). Square it (0.4982698963) and add it to both sides. Add '0.4982698963' to each side of the equation. -1.411764706x + 0.4982698963 + x2 = -0.4705882353 + 0.4982698963 Reorder the terms: 0.4982698963 + -1.411764706x + x2 = -0.4705882353 + 0.4982698963 Combine like terms: -0.4705882353 + 0.4982698963 = 0.027681661 0.4982698963 + -1.411764706x + x2 = 0.027681661 Factor a perfect square on the left side: (x + -0.705882353)(x + -0.705882353) = 0.027681661 Calculate the square root of the right side: 0.166378066 Break this problem into two subproblems by setting (x + -0.705882353) equal to 0.166378066 and -0.166378066.Subproblem 1
x + -0.705882353 = 0.166378066 Simplifying x + -0.705882353 = 0.166378066 Reorder the terms: -0.705882353 + x = 0.166378066 Solving -0.705882353 + x = 0.166378066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.705882353' to each side of the equation. -0.705882353 + 0.705882353 + x = 0.166378066 + 0.705882353 Combine like terms: -0.705882353 + 0.705882353 = 0.000000000 0.000000000 + x = 0.166378066 + 0.705882353 x = 0.166378066 + 0.705882353 Combine like terms: 0.166378066 + 0.705882353 = 0.872260419 x = 0.872260419 Simplifying x = 0.872260419Subproblem 2
x + -0.705882353 = -0.166378066 Simplifying x + -0.705882353 = -0.166378066 Reorder the terms: -0.705882353 + x = -0.166378066 Solving -0.705882353 + x = -0.166378066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.705882353' to each side of the equation. -0.705882353 + 0.705882353 + x = -0.166378066 + 0.705882353 Combine like terms: -0.705882353 + 0.705882353 = 0.000000000 0.000000000 + x = -0.166378066 + 0.705882353 x = -0.166378066 + 0.705882353 Combine like terms: -0.166378066 + 0.705882353 = 0.539504287 x = 0.539504287 Simplifying x = 0.539504287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.872260419, 0.539504287}
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