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Simplifying 4x2 + -39x + 59 = 0 Reorder the terms: 59 + -39x + 4x2 = 0 Solving 59 + -39x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 14.75 + -9.75x + x2 = 0 Move the constant term to the right: Add '-14.75' to each side of the equation. 14.75 + -9.75x + -14.75 + x2 = 0 + -14.75 Reorder the terms: 14.75 + -14.75 + -9.75x + x2 = 0 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + -9.75x + x2 = 0 + -14.75 -9.75x + x2 = 0 + -14.75 Combine like terms: 0 + -14.75 = -14.75 -9.75x + x2 = -14.75 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -14.75 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -14.75 + 23.765625 Combine like terms: -14.75 + 23.765625 = 9.015625 23.765625 + -9.75x + x2 = 9.015625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 9.015625 Calculate the square root of the right side: 3.002603037 Break this problem into two subproblems by setting (x + -4.875) equal to 3.002603037 and -3.002603037.Subproblem 1
x + -4.875 = 3.002603037 Simplifying x + -4.875 = 3.002603037 Reorder the terms: -4.875 + x = 3.002603037 Solving -4.875 + x = 3.002603037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 3.002603037 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 3.002603037 + 4.875 x = 3.002603037 + 4.875 Combine like terms: 3.002603037 + 4.875 = 7.877603037 x = 7.877603037 Simplifying x = 7.877603037Subproblem 2
x + -4.875 = -3.002603037 Simplifying x + -4.875 = -3.002603037 Reorder the terms: -4.875 + x = -3.002603037 Solving -4.875 + x = -3.002603037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -3.002603037 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -3.002603037 + 4.875 x = -3.002603037 + 4.875 Combine like terms: -3.002603037 + 4.875 = 1.872396963 x = 1.872396963 Simplifying x = 1.872396963Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.877603037, 1.872396963}
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