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Simplifying 0 = x2 + -18x + 34 Reorder the terms: 0 = 34 + -18x + x2 Solving 0 = 34 + -18x + x2 Solving for variable 'x'. Combine like terms: 0 + -34 = -34 -34 + 18x + -1x2 = 34 + -18x + x2 + -34 + 18x + -1x2 Reorder the terms: -34 + 18x + -1x2 = 34 + -34 + -18x + 18x + x2 + -1x2 Combine like terms: 34 + -34 = 0 -34 + 18x + -1x2 = 0 + -18x + 18x + x2 + -1x2 -34 + 18x + -1x2 = -18x + 18x + x2 + -1x2 Combine like terms: -18x + 18x = 0 -34 + 18x + -1x2 = 0 + x2 + -1x2 -34 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -34 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 34 + -18x + x2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + -18x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -18x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -18x + x2 = 0 + -34 -18x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -18x + x2 = -34 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 = -34 + 81 Reorder the terms: 81 + -18x + x2 = -34 + 81 Combine like terms: -34 + 81 = 47 81 + -18x + x2 = 47 Factor a perfect square on the left side: (x + -9)(x + -9) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -9) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -9 = 6.8556546 Simplifying x + -9 = 6.8556546 Reorder the terms: -9 + x = 6.8556546 Solving -9 + x = 6.8556546 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 = 6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + x = 6.8556546 + 9 x = 6.8556546 + 9 Combine like terms: 6.8556546 + 9 = 15.8556546 x = 15.8556546 Simplifying x = 15.8556546Subproblem 2
x + -9 = -6.8556546 Simplifying x + -9 = -6.8556546 Reorder the terms: -9 + x = -6.8556546 Solving -9 + x = -6.8556546 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 = -6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + x = -6.8556546 + 9 x = -6.8556546 + 9 Combine like terms: -6.8556546 + 9 = 2.1443454 x = 2.1443454 Simplifying x = 2.1443454Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.8556546, 2.1443454}
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