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Simplifying 4y2 = (11y + -1)(11y + -1) Reorder the terms: 4y2 = (-1 + 11y)(11y + -1) Reorder the terms: 4y2 = (-1 + 11y)(-1 + 11y) Multiply (-1 + 11y) * (-1 + 11y) 4y2 = (-1(-1 + 11y) + 11y * (-1 + 11y)) 4y2 = ((-1 * -1 + 11y * -1) + 11y * (-1 + 11y)) 4y2 = ((1 + -11y) + 11y * (-1 + 11y)) 4y2 = (1 + -11y + (-1 * 11y + 11y * 11y)) 4y2 = (1 + -11y + (-11y + 121y2)) Combine like terms: -11y + -11y = -22y 4y2 = (1 + -22y + 121y2) Solving 4y2 = 1 + -22y + 121y2 Solving for variable 'y'. Reorder the terms: -1 + 22y + 4y2 + -121y2 = 1 + -22y + 121y2 + -1 + 22y + -121y2 Combine like terms: 4y2 + -121y2 = -117y2 -1 + 22y + -117y2 = 1 + -22y + 121y2 + -1 + 22y + -121y2 Reorder the terms: -1 + 22y + -117y2 = 1 + -1 + -22y + 22y + 121y2 + -121y2 Combine like terms: 1 + -1 = 0 -1 + 22y + -117y2 = 0 + -22y + 22y + 121y2 + -121y2 -1 + 22y + -117y2 = -22y + 22y + 121y2 + -121y2 Combine like terms: -22y + 22y = 0 -1 + 22y + -117y2 = 0 + 121y2 + -121y2 -1 + 22y + -117y2 = 121y2 + -121y2 Combine like terms: 121y2 + -121y2 = 0 -1 + 22y + -117y2 = 0 Factor a trinomial. (-1 + 9y)(1 + -13y) = 0Subproblem 1
Set the factor '(-1 + 9y)' equal to zero and attempt to solve: Simplifying -1 + 9y = 0 Solving -1 + 9y = 0 Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 9y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 9y = 0 + 1 9y = 0 + 1 Combine like terms: 0 + 1 = 1 9y = 1 Divide each side by '9'. y = 0.1111111111 Simplifying y = 0.1111111111Subproblem 2
Set the factor '(1 + -13y)' equal to zero and attempt to solve: Simplifying 1 + -13y = 0 Solving 1 + -13y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -13y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -13y = 0 + -1 -13y = 0 + -1 Combine like terms: 0 + -1 = -1 -13y = -1 Divide each side by '-13'. y = 0.07692307692 Simplifying y = 0.07692307692Solution
y = {0.1111111111, 0.07692307692}
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