2x^2=5x+52

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Solution for 2x^2=5x+52 equation:


Simplifying
2x2 = 5x + 52

Reorder the terms:
2x2 = 52 + 5x

Solving
2x2 = 52 + 5x

Solving for variable 'x'.

Reorder the terms:
-52 + -5x + 2x2 = 52 + 5x + -52 + -5x

Reorder the terms:
-52 + -5x + 2x2 = 52 + -52 + 5x + -5x

Combine like terms: 52 + -52 = 0
-52 + -5x + 2x2 = 0 + 5x + -5x
-52 + -5x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-52 + -5x + 2x2 = 0

Factor a trinomial.
(-4 + -1x)(13 + -2x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(13 + -2x)' equal to zero and attempt to solve: Simplifying 13 + -2x = 0 Solving 13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2x = 0 + -13 -2x = 0 + -13 Combine like terms: 0 + -13 = -13 -2x = -13 Divide each side by '-2'. x = 6.5 Simplifying x = 6.5

Solution

x = {-4, 6.5}

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