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Simplifying (6x7 + 6x5)(3x8 + -9x6) = 0 Reorder the terms: (6x5 + 6x7)(3x8 + -9x6) = 0 Reorder the terms: (6x5 + 6x7)(-9x6 + 3x8) = 0 Multiply (6x5 + 6x7) * (-9x6 + 3x8) (6x5 * (-9x6 + 3x8) + 6x7 * (-9x6 + 3x8)) = 0 ((-9x6 * 6x5 + 3x8 * 6x5) + 6x7 * (-9x6 + 3x8)) = 0 ((-54x11 + 18x13) + 6x7 * (-9x6 + 3x8)) = 0 (-54x11 + 18x13 + (-9x6 * 6x7 + 3x8 * 6x7)) = 0 (-54x11 + 18x13 + (-54x13 + 18x15)) = 0 Combine like terms: 18x13 + -54x13 = -36x13 (-54x11 + -36x13 + 18x15) = 0 Solving -54x11 + -36x13 + 18x15 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '18x11'. 18x11(-3 + -2x2 + x4) = 0 Factor a trinomial. 18x11((-1 + -1x2)(3 + -1x2)) = 0 Ignore the factor 18.Subproblem 1
Set the factor 'x11' equal to zero and attempt to solve: Simplifying x11 = 0 Solving x11 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x11 = 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 '(-1 + -1x2)' equal to zero and attempt to solve: Simplifying -1 + -1x2 = 0 Solving -1 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x2 = 0 + 1 -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x2 = 1 Divide each side by '-1'. x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -1x2 = 0 Solving 3 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x2 = 0 + -3 -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x2 = -3 Divide each side by '-1'. x2 = 3 Simplifying x2 = 3 Take the square root of each side: x = {-1.732050808, 1.732050808}Solution
x = {-1.732050808, 1.732050808}
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