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Simplifying 13x2 + 234x + 1035 = 0 Reorder the terms: 1035 + 234x + 13x2 = 0 Solving 1035 + 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'. 79.61538462 + 18x + x2 = 0 Move the constant term to the right: Add '-79.61538462' to each side of the equation. 79.61538462 + 18x + -79.61538462 + x2 = 0 + -79.61538462 Reorder the terms: 79.61538462 + -79.61538462 + 18x + x2 = 0 + -79.61538462 Combine like terms: 79.61538462 + -79.61538462 = 0.00000000 0.00000000 + 18x + x2 = 0 + -79.61538462 18x + x2 = 0 + -79.61538462 Combine like terms: 0 + -79.61538462 = -79.61538462 18x + x2 = -79.61538462 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 = -79.61538462 + 81 Reorder the terms: 81 + 18x + x2 = -79.61538462 + 81 Combine like terms: -79.61538462 + 81 = 1.38461538 81 + 18x + x2 = 1.38461538 Factor a perfect square on the left side: (x + 9)(x + 9) = 1.38461538 Calculate the square root of the right side: 1.176696809 Break this problem into two subproblems by setting (x + 9) equal to 1.176696809 and -1.176696809.Subproblem 1
x + 9 = 1.176696809 Simplifying x + 9 = 1.176696809 Reorder the terms: 9 + x = 1.176696809 Solving 9 + x = 1.176696809 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 = 1.176696809 + -9 Combine like terms: 9 + -9 = 0 0 + x = 1.176696809 + -9 x = 1.176696809 + -9 Combine like terms: 1.176696809 + -9 = -7.823303191 x = -7.823303191 Simplifying x = -7.823303191Subproblem 2
x + 9 = -1.176696809 Simplifying x + 9 = -1.176696809 Reorder the terms: 9 + x = -1.176696809 Solving 9 + x = -1.176696809 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 = -1.176696809 + -9 Combine like terms: 9 + -9 = 0 0 + x = -1.176696809 + -9 x = -1.176696809 + -9 Combine like terms: -1.176696809 + -9 = -10.176696809 x = -10.176696809 Simplifying x = -10.176696809Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.823303191, -10.176696809}
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