2y^2=25y+13

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Solution for 2y^2=25y+13 equation:


Simplifying
2y2 = 25y + 13

Reorder the terms:
2y2 = 13 + 25y

Solving
2y2 = 13 + 25y

Solving for variable 'y'.

Reorder the terms:
-13 + -25y + 2y2 = 13 + 25y + -13 + -25y

Reorder the terms:
-13 + -25y + 2y2 = 13 + -13 + 25y + -25y

Combine like terms: 13 + -13 = 0
-13 + -25y + 2y2 = 0 + 25y + -25y
-13 + -25y + 2y2 = 25y + -25y

Combine like terms: 25y + -25y = 0
-13 + -25y + 2y2 = 0

Factor a trinomial.
(-1 + -2y)(13 + -1y) = 0

Subproblem 1

Set the factor '(-1 + -2y)' equal to zero and attempt to solve: Simplifying -1 + -2y = 0 Solving -1 + -2y = 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 + -2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2y = 0 + 1 -2y = 0 + 1 Combine like terms: 0 + 1 = 1 -2y = 1 Divide each side by '-2'. y = -0.5 Simplifying y = -0.5

Subproblem 2

Set the factor '(13 + -1y)' equal to zero and attempt to solve: Simplifying 13 + -1y = 0 Solving 13 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1y = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1y = 0 + -13 -1y = 0 + -13 Combine like terms: 0 + -13 = -13 -1y = -13 Divide each side by '-1'. y = 13 Simplifying y = 13

Solution

y = {-0.5, 13}

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