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Simplifying 10x(6x2 + 7x + 9) = 0 Reorder the terms: 10x(9 + 7x + 6x2) = 0 (9 * 10x + 7x * 10x + 6x2 * 10x) = 0 (90x + 70x2 + 60x3) = 0 Solving 90x + 70x2 + 60x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(9 + 7x + 6x2) = 0 Ignore the factor 10.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 = -1.159722222 0.3402777780 + 1.166666667x + x2 = -1.159722222 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = -1.159722222 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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