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Simplifying 13x2 + -234x + 1052 = 0 Reorder the terms: 1052 + -234x + 13x2 = 0 Solving 1052 + -234x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 80.92307692 + -18x + x2 = 0 Move the constant term to the right: Add '-80.92307692' to each side of the equation. 80.92307692 + -18x + -80.92307692 + x2 = 0 + -80.92307692 Reorder the terms: 80.92307692 + -80.92307692 + -18x + x2 = 0 + -80.92307692 Combine like terms: 80.92307692 + -80.92307692 = 0.00000000 0.00000000 + -18x + x2 = 0 + -80.92307692 -18x + x2 = 0 + -80.92307692 Combine like terms: 0 + -80.92307692 = -80.92307692 -18x + x2 = -80.92307692 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -80.92307692 + 81 Reorder the terms: 81 + -18x + x2 = -80.92307692 + 81 Combine like terms: -80.92307692 + 81 = 0.07692308 81 + -18x + x2 = 0.07692308 Factor a perfect square on the left side: (x + -9)(x + -9) = 0.07692308 Calculate the square root of the right side: 0.277350104 Break this problem into two subproblems by setting (x + -9) equal to 0.277350104 and -0.277350104.Subproblem 1
x + -9 = 0.277350104 Simplifying x + -9 = 0.277350104 Reorder the terms: -9 + x = 0.277350104 Solving -9 + x = 0.277350104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0.277350104 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0.277350104 + 9 x = 0.277350104 + 9 Combine like terms: 0.277350104 + 9 = 9.277350104 x = 9.277350104 Simplifying x = 9.277350104Subproblem 2
x + -9 = -0.277350104 Simplifying x + -9 = -0.277350104 Reorder the terms: -9 + x = -0.277350104 Solving -9 + x = -0.277350104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -0.277350104 + 9 Combine like terms: -9 + 9 = 0 0 + x = -0.277350104 + 9 x = -0.277350104 + 9 Combine like terms: -0.277350104 + 9 = 8.722649896 x = 8.722649896 Simplifying x = 8.722649896Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.277350104, 8.722649896}
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