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Simplifying 12x3 + 10x2 + 14x = 0 Reorder the terms: 14x + 10x2 + 12x3 = 0 Solving 14x + 10x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(7 + 5x + 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 '(7 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying 7 + 5x + 6x2 = 0 Solving 7 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 0.8333333333x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 0.8333333333x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 0.8333333333x + x2 = 0 + -1.166666667 0.8333333333x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 0.8333333333x + x2 = -1.166666667 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = -1.166666667 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -1.166666667 + 0.1736111111 Combine like terms: -1.166666667 + 0.1736111111 = -0.9930555559 0.1736111111 + 0.8333333333x + x2 = -0.9930555559 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -0.9930555559 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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