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Simplifying 9x2(x2 + 6xy + -7y2) = 0 Reorder the terms: 9x2(6xy + x2 + -7y2) = 0 (6xy * 9x2 + x2 * 9x2 + -7y2 * 9x2) = 0 Reorder the terms: (-63x2y2 + 54x3y + 9x4) = 0 (-63x2y2 + 54x3y + 9x4) = 0 Solving -63x2y2 + 54x3y + 9x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9x2'. 9x2(-7y2 + 6xy + x2) = 0 Factor a trinomial. 9x2((-7y + -1x)(y + -1x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-7y + -1x)' equal to zero and attempt to solve: Simplifying -7y + -1x = 0 Reorder the terms: -1x + -7y = 0 Solving -1x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. -1x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 -1x + 0 = 0 + 7y -1x = 0 + 7y Remove the zero: -1x = 7y Divide each side by '-1'. x = -7y Simplifying x = -7ySubproblem 3
Set the factor '(y + -1x)' equal to zero and attempt to solve: Simplifying y + -1x = 0 Reorder the terms: -1x + y = 0 Solving -1x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -1x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -1x + 0 = 0 + -1y -1x = 0 + -1y Remove the zero: -1x = -1y Divide each side by '-1'. x = y Simplifying x = ySolution
x = {0, -7y, y}
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