y^2=9y-14

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Solution for y^2=9y-14 equation:


Simplifying
y2 = 9y + -14

Reorder the terms:
y2 = -14 + 9y

Solving
y2 = -14 + 9y

Solving for variable 'y'.

Reorder the terms:
14 + -9y + y2 = -14 + 9y + 14 + -9y

Reorder the terms:
14 + -9y + y2 = -14 + 14 + 9y + -9y

Combine like terms: -14 + 14 = 0
14 + -9y + y2 = 0 + 9y + -9y
14 + -9y + y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
14 + -9y + y2 = 0

Factor a trinomial.
(2 + -1y)(7 + -1y) = 0

Subproblem 1

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Subproblem 2

Set the factor '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7

Solution

y = {2, 7}

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