5y^2+34y=7

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Solution for 5y^2+34y=7 equation:


Simplifying
5y2 + 34y = 7

Reorder the terms:
34y + 5y2 = 7

Solving
34y + 5y2 = 7

Solving for variable 'y'.

Reorder the terms:
-7 + 34y + 5y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 34y + 5y2 = 0

Factor a trinomial.
(-7 + -1y)(1 + -5y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -5y)' equal to zero and attempt to solve: Simplifying 1 + -5y = 0 Solving 1 + -5y = 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 + -5y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5y = 0 + -1 -5y = 0 + -1 Combine like terms: 0 + -1 = -1 -5y = -1 Divide each side by '-5'. y = 0.2 Simplifying y = 0.2

Solution

y = {-7, 0.2}

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