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Simplifying 12x2 + -14x + -240 = 0 Reorder the terms: -240 + -14x + 12x2 = 0 Solving -240 + -14x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-120 + -7x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-120 + -7x + 6x2)' equal to zero and attempt to solve: Simplifying -120 + -7x + 6x2 = 0 Solving -120 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -20 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -1.166666667x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -1.166666667x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1.166666667x + x2 = 0 + 20 -1.166666667x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -1.166666667x + x2 = 20 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 = 20 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 20 + 0.3402777780 Combine like terms: 20 + 0.3402777780 = 20.340277778 0.3402777780 + -1.166666667x + x2 = 20.340277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 20.340277778 Calculate the square root of the right side: 4.510019709 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 4.510019709 and -4.510019709.Subproblem 1
x + -0.5833333335 = 4.510019709 Simplifying x + -0.5833333335 = 4.510019709 Reorder the terms: -0.5833333335 + x = 4.510019709 Solving -0.5833333335 + x = 4.510019709 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 = 4.510019709 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 4.510019709 + 0.5833333335 x = 4.510019709 + 0.5833333335 Combine like terms: 4.510019709 + 0.5833333335 = 5.0933530425 x = 5.0933530425 Simplifying x = 5.0933530425Subproblem 2
x + -0.5833333335 = -4.510019709 Simplifying x + -0.5833333335 = -4.510019709 Reorder the terms: -0.5833333335 + x = -4.510019709 Solving -0.5833333335 + x = -4.510019709 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 = -4.510019709 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -4.510019709 + 0.5833333335 x = -4.510019709 + 0.5833333335 Combine like terms: -4.510019709 + 0.5833333335 = -3.9266863755 x = -3.9266863755 Simplifying x = -3.9266863755Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.0933530425, -3.9266863755}Solution
x = {5.0933530425, -3.9266863755}
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