2t^2=t+36

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Solution for 2t^2=t+36 equation:


Simplifying
2t2 = t + 36

Reorder the terms:
2t2 = 36 + t

Solving
2t2 = 36 + t

Solving for variable 't'.

Reorder the terms:
-36 + -1t + 2t2 = 36 + t + -36 + -1t

Reorder the terms:
-36 + -1t + 2t2 = 36 + -36 + t + -1t

Combine like terms: 36 + -36 = 0
-36 + -1t + 2t2 = 0 + t + -1t
-36 + -1t + 2t2 = t + -1t

Combine like terms: t + -1t = 0
-36 + -1t + 2t2 = 0

Factor a trinomial.
(-4 + -1t)(9 + -2t) = 0

Subproblem 1

Set the factor '(-4 + -1t)' equal to zero and attempt to solve: Simplifying -4 + -1t = 0 Solving -4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1t = 0 + 4 -1t = 0 + 4 Combine like terms: 0 + 4 = 4 -1t = 4 Divide each side by '-1'. t = -4 Simplifying t = -4

Subproblem 2

Set the factor '(9 + -2t)' equal to zero and attempt to solve: Simplifying 9 + -2t = 0 Solving 9 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2t = 0 + -9 -2t = 0 + -9 Combine like terms: 0 + -9 = -9 -2t = -9 Divide each side by '-2'. t = 4.5 Simplifying t = 4.5

Solution

t = {-4, 4.5}

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