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Simplifying 12x3 + 14x2 + -18x = 0 Reorder the terms: -18x + 14x2 + 12x3 = 0 Solving -18x + 14x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-9 + 7x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-9 + 7x + 6x2)' equal to zero and attempt to solve: Simplifying -9 + 7x + 6x2 = 0 Solving -9 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 1.166666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 1.166666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 1.166666667x + x2 = 0 + 1.5 1.166666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 1.166666667x + x2 = 1.5 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 = 1.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 1.5 + 0.3402777780 Combine like terms: 1.5 + 0.3402777780 = 1.840277778 0.3402777780 + 1.166666667x + x2 = 1.840277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 1.840277778 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.356568383 and -1.356568383.Subproblem 1
x + 0.5833333335 = 1.356568383 Simplifying x + 0.5833333335 = 1.356568383 Reorder the terms: 0.5833333335 + x = 1.356568383 Solving 0.5833333335 + x = 1.356568383 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 = 1.356568383 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.356568383 + -0.5833333335 x = 1.356568383 + -0.5833333335 Combine like terms: 1.356568383 + -0.5833333335 = 0.7732350495 x = 0.7732350495 Simplifying x = 0.7732350495Subproblem 2
x + 0.5833333335 = -1.356568383 Simplifying x + 0.5833333335 = -1.356568383 Reorder the terms: 0.5833333335 + x = -1.356568383 Solving 0.5833333335 + x = -1.356568383 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 = -1.356568383 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.356568383 + -0.5833333335 x = -1.356568383 + -0.5833333335 Combine like terms: -1.356568383 + -0.5833333335 = -1.9399017165 x = -1.9399017165 Simplifying x = -1.9399017165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7732350495, -1.9399017165}Solution
x = {0, 0.7732350495, -1.9399017165}
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