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Simplifying -5x6(6x3 + -5x2 + -9x) = 0 Reorder the terms: -5x6(-9x + -5x2 + 6x3) = 0 (-9x * -5x6 + -5x2 * -5x6 + 6x3 * -5x6) = 0 (45x7 + 25x8 + -30x9) = 0 Solving 45x7 + 25x8 + -30x9 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x7'. 5x7(9 + 5x + -6x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x7' equal to zero and attempt to solve: Simplifying x7 = 0 Solving x7 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x7 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(9 + 5x + -6x2)' equal to zero and attempt to solve: Simplifying 9 + 5x + -6x2 = 0 Solving 9 + 5x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.5 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.8333333333x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.8333333333x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.8333333333x + x2 = 0 + 1.5 -0.8333333333x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.8333333333x + x2 = 1.5 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 = 1.5 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 1.5 + 0.1736111111 Combine like terms: 1.5 + 0.1736111111 = 1.6736111111 0.1736111111 + -0.8333333333x + x2 = 1.6736111111 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 1.6736111111 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 1.293681225 and -1.293681225.Subproblem 1
x + -0.4166666667 = 1.293681225 Simplifying x + -0.4166666667 = 1.293681225 Reorder the terms: -0.4166666667 + x = 1.293681225 Solving -0.4166666667 + x = 1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 1.293681225 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 1.293681225 + 0.4166666667 x = 1.293681225 + 0.4166666667 Combine like terms: 1.293681225 + 0.4166666667 = 1.7103478917 x = 1.7103478917 Simplifying x = 1.7103478917Subproblem 2
x + -0.4166666667 = -1.293681225 Simplifying x + -0.4166666667 = -1.293681225 Reorder the terms: -0.4166666667 + x = -1.293681225 Solving -0.4166666667 + x = -1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -1.293681225 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -1.293681225 + 0.4166666667 x = -1.293681225 + 0.4166666667 Combine like terms: -1.293681225 + 0.4166666667 = -0.8770145583 x = -0.8770145583 Simplifying x = -0.8770145583Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7103478917, -0.8770145583}Solution
x = {1.7103478917, -0.8770145583}
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