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Simplifying 15 = 18x2 + -14x Reorder the terms: 15 = -14x + 18x2 Solving 15 = -14x + 18x2 Solving for variable 'x'. Reorder the terms: 15 + 14x + -18x2 = -14x + 14x + 18x2 + -18x2 Combine like terms: -14x + 14x = 0 15 + 14x + -18x2 = 0 + 18x2 + -18x2 15 + 14x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 15 + 14x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.8333333333 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.7777777778x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.7777777778x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.7777777778x + x2 = 0 + 0.8333333333 -0.7777777778x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.7777777778x + x2 = 0.8333333333 The x term is -0.7777777778x. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778x + 0.1512345679 + x2 = 0.8333333333 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 0.8333333333 + 0.1512345679 Combine like terms: 0.8333333333 + 0.1512345679 = 0.9845679012 0.1512345679 + -0.7777777778x + x2 = 0.9845679012 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 0.9845679012 Calculate the square root of the right side: 0.99225395 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 0.99225395 and -0.99225395.Subproblem 1
x + -0.3888888889 = 0.99225395 Simplifying x + -0.3888888889 = 0.99225395 Reorder the terms: -0.3888888889 + x = 0.99225395 Solving -0.3888888889 + x = 0.99225395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = 0.99225395 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 0.99225395 + 0.3888888889 x = 0.99225395 + 0.3888888889 Combine like terms: 0.99225395 + 0.3888888889 = 1.3811428389 x = 1.3811428389 Simplifying x = 1.3811428389Subproblem 2
x + -0.3888888889 = -0.99225395 Simplifying x + -0.3888888889 = -0.99225395 Reorder the terms: -0.3888888889 + x = -0.99225395 Solving -0.3888888889 + x = -0.99225395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = -0.99225395 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -0.99225395 + 0.3888888889 x = -0.99225395 + 0.3888888889 Combine like terms: -0.99225395 + 0.3888888889 = -0.6033650611 x = -0.6033650611 Simplifying x = -0.6033650611Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3811428389, -0.6033650611}
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