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Simplifying 12x2 + 14x + -15 = 0 Reorder the terms: -15 + 14x + 12x2 = 0 Solving -15 + 14x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.25 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.166666667x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.166666667x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.166666667x + x2 = 0 + 1.25 1.166666667x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.166666667x + x2 = 1.25 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 1.25 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 1.25 + 0.3402777780 Combine like terms: 1.25 + 0.3402777780 = 1.590277778 0.3402777780 + 1.166666667x + x2 = 1.590277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 1.590277778 Calculate the square root of the right side: 1.261062163 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.261062163 and -1.261062163.Subproblem 1
x + 0.5833333335 = 1.261062163 Simplifying x + 0.5833333335 = 1.261062163 Reorder the terms: 0.5833333335 + x = 1.261062163 Solving 0.5833333335 + x = 1.261062163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 1.261062163 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.261062163 + -0.5833333335 x = 1.261062163 + -0.5833333335 Combine like terms: 1.261062163 + -0.5833333335 = 0.6777288295 x = 0.6777288295 Simplifying x = 0.6777288295Subproblem 2
x + 0.5833333335 = -1.261062163 Simplifying x + 0.5833333335 = -1.261062163 Reorder the terms: 0.5833333335 + x = -1.261062163 Solving 0.5833333335 + x = -1.261062163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -1.261062163 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.261062163 + -0.5833333335 x = -1.261062163 + -0.5833333335 Combine like terms: -1.261062163 + -0.5833333335 = -1.8443954965 x = -1.8443954965 Simplifying x = -1.8443954965Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6777288295, -1.8443954965}
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