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Simplifying 6y + x2 = 91y2 Reorder the terms: x2 + 6y = 91y2 Solving x2 + 6y = 91y2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. x2 + 6y + -6y = -6y + 91y2 Combine like terms: 6y + -6y = 0 x2 + 0 = -6y + 91y2 x2 = -6y + 91y2 Simplifying x2 = -6y + 91y2 Reorder the terms: x2 + 6y + -91y2 = -6y + 6y + 91y2 + -91y2 Combine like terms: -6y + 6y = 0 x2 + 6y + -91y2 = 0 + 91y2 + -91y2 x2 + 6y + -91y2 = 91y2 + -91y2 Combine like terms: 91y2 + -91y2 = 0 x2 + 6y + -91y2 = 0 Factor a trinomial. (x + -7y)(x + 13y) = 0Subproblem 1
Set the factor '(x + -7y)' equal to zero and attempt to solve: Simplifying x + -7y = 0 Solving x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 x + 0 = 0 + 7y x = 0 + 7y Remove the zero: x = 7y Simplifying x = 7ySubproblem 2
Set the factor '(x + 13y)' equal to zero and attempt to solve: Simplifying x + 13y = 0 Solving x + 13y = 0 Move all terms containing x to the left, all other terms to the right. Add '-13y' to each side of the equation. x + 13y + -13y = 0 + -13y Combine like terms: 13y + -13y = 0 x + 0 = 0 + -13y x = 0 + -13y Remove the zero: x = -13y Simplifying x = -13ySolution
x = {7y, -13y}
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