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Simplifying 18x2 + 32x + -660 = 0 Reorder the terms: -660 + 32x + 18x2 = 0 Solving -660 + 32x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-330 + 16x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-330 + 16x + 9x2)' equal to zero and attempt to solve: Simplifying -330 + 16x + 9x2 = 0 Solving -330 + 16x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -36.66666667 + 1.777777778x + x2 = 0 Move the constant term to the right: Add '36.66666667' to each side of the equation. -36.66666667 + 1.777777778x + 36.66666667 + x2 = 0 + 36.66666667 Reorder the terms: -36.66666667 + 36.66666667 + 1.777777778x + x2 = 0 + 36.66666667 Combine like terms: -36.66666667 + 36.66666667 = 0.00000000 0.00000000 + 1.777777778x + x2 = 0 + 36.66666667 1.777777778x + x2 = 0 + 36.66666667 Combine like terms: 0 + 36.66666667 = 36.66666667 1.777777778x + x2 = 36.66666667 The x term is 1.777777778x. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778x + 0.7901234570 + x2 = 36.66666667 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778x + x2 = 36.66666667 + 0.7901234570 Combine like terms: 36.66666667 + 0.7901234570 = 37.456790127 0.7901234570 + 1.777777778x + x2 = 37.456790127 Factor a perfect square on the left side: (x + 0.888888889)(x + 0.888888889) = 37.456790127 Calculate the square root of the right side: 6.120195269 Break this problem into two subproblems by setting (x + 0.888888889) equal to 6.120195269 and -6.120195269.Subproblem 1
x + 0.888888889 = 6.120195269 Simplifying x + 0.888888889 = 6.120195269 Reorder the terms: 0.888888889 + x = 6.120195269 Solving 0.888888889 + x = 6.120195269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = 6.120195269 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = 6.120195269 + -0.888888889 x = 6.120195269 + -0.888888889 Combine like terms: 6.120195269 + -0.888888889 = 5.23130638 x = 5.23130638 Simplifying x = 5.23130638Subproblem 2
x + 0.888888889 = -6.120195269 Simplifying x + 0.888888889 = -6.120195269 Reorder the terms: 0.888888889 + x = -6.120195269 Solving 0.888888889 + x = -6.120195269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = -6.120195269 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = -6.120195269 + -0.888888889 x = -6.120195269 + -0.888888889 Combine like terms: -6.120195269 + -0.888888889 = -7.009084158 x = -7.009084158 Simplifying x = -7.009084158Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.23130638, -7.009084158}Solution
x = {5.23130638, -7.009084158}
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