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Simplifying 2x2 + -8x + -11 + x2 + -3x + 13 = 180 Reorder the terms: -11 + 13 + -8x + -3x + 2x2 + x2 = 180 Combine like terms: -11 + 13 = 2 2 + -8x + -3x + 2x2 + x2 = 180 Combine like terms: -8x + -3x = -11x 2 + -11x + 2x2 + x2 = 180 Combine like terms: 2x2 + x2 = 3x2 2 + -11x + 3x2 = 180 Solving 2 + -11x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 2 + -180 + -11x + 3x2 = 180 + -180 Combine like terms: 2 + -180 = -178 -178 + -11x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -178 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -59.33333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '59.33333333' to each side of the equation. -59.33333333 + -3.666666667x + 59.33333333 + x2 = 0 + 59.33333333 Reorder the terms: -59.33333333 + 59.33333333 + -3.666666667x + x2 = 0 + 59.33333333 Combine like terms: -59.33333333 + 59.33333333 = 0.00000000 0.00000000 + -3.666666667x + x2 = 0 + 59.33333333 -3.666666667x + x2 = 0 + 59.33333333 Combine like terms: 0 + 59.33333333 = 59.33333333 -3.666666667x + x2 = 59.33333333 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 59.33333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 59.33333333 + 3.361111114 Combine like terms: 59.33333333 + 3.361111114 = 62.694444444 3.361111114 + -3.666666667x + x2 = 62.694444444 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 62.694444444 Calculate the square root of the right side: 7.917982347 Break this problem into two subproblems by setting (x + -1.833333334) equal to 7.917982347 and -7.917982347.Subproblem 1
x + -1.833333334 = 7.917982347 Simplifying x + -1.833333334 = 7.917982347 Reorder the terms: -1.833333334 + x = 7.917982347 Solving -1.833333334 + x = 7.917982347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 7.917982347 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 7.917982347 + 1.833333334 x = 7.917982347 + 1.833333334 Combine like terms: 7.917982347 + 1.833333334 = 9.751315681 x = 9.751315681 Simplifying x = 9.751315681Subproblem 2
x + -1.833333334 = -7.917982347 Simplifying x + -1.833333334 = -7.917982347 Reorder the terms: -1.833333334 + x = -7.917982347 Solving -1.833333334 + x = -7.917982347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -7.917982347 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -7.917982347 + 1.833333334 x = -7.917982347 + 1.833333334 Combine like terms: -7.917982347 + 1.833333334 = -6.084649013 x = -6.084649013 Simplifying x = -6.084649013Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.751315681, -6.084649013}
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