5x^2=11x+36

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Solution for 5x^2=11x+36 equation:


Simplifying
5x2 = 11x + 36

Reorder the terms:
5x2 = 36 + 11x

Solving
5x2 = 36 + 11x

Solving for variable 'x'.

Reorder the terms:
-36 + -11x + 5x2 = 36 + 11x + -36 + -11x

Reorder the terms:
-36 + -11x + 5x2 = 36 + -36 + 11x + -11x

Combine like terms: 36 + -36 = 0
-36 + -11x + 5x2 = 0 + 11x + -11x
-36 + -11x + 5x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-36 + -11x + 5x2 = 0

Factor a trinomial.
(-9 + -5x)(4 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -5x)' equal to zero and attempt to solve: Simplifying -9 + -5x = 0 Solving -9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5x = 0 + 9 -5x = 0 + 9 Combine like terms: 0 + 9 = 9 -5x = 9 Divide each side by '-5'. x = -1.8 Simplifying x = -1.8

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-1.8, 4}

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