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Simplifying 180x2 + -210x + -60 = 0 Reorder the terms: -60 + -210x + 180x2 = 0 Solving -60 + -210x + 180x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '30'. 30(-2 + -7x + 6x2) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(-2 + -7x + 6x2)' equal to zero and attempt to solve: Simplifying -2 + -7x + 6x2 = 0 Solving -2 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.166666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.166666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + 0.3333333333 -1.166666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.166666667x + x2 = 0.3333333333 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 = 0.3333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.3333333333 + 0.3402777780 Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113 0.3402777780 + -1.166666667x + x2 = 0.6736111113 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.6736111113 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.82073815 and -0.82073815.Subproblem 1
x + -0.5833333335 = 0.82073815 Simplifying x + -0.5833333335 = 0.82073815 Reorder the terms: -0.5833333335 + x = 0.82073815 Solving -0.5833333335 + x = 0.82073815 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 = 0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.82073815 + 0.5833333335 x = 0.82073815 + 0.5833333335 Combine like terms: 0.82073815 + 0.5833333335 = 1.4040714835 x = 1.4040714835 Simplifying x = 1.4040714835Subproblem 2
x + -0.5833333335 = -0.82073815 Simplifying x + -0.5833333335 = -0.82073815 Reorder the terms: -0.5833333335 + x = -0.82073815 Solving -0.5833333335 + x = -0.82073815 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 = -0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.82073815 + 0.5833333335 x = -0.82073815 + 0.5833333335 Combine like terms: -0.82073815 + 0.5833333335 = -0.2374048165 x = -0.2374048165 Simplifying x = -0.2374048165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4040714835, -0.2374048165}Solution
x = {1.4040714835, -0.2374048165}
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