2x^2=54-3x

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Solution for 2x^2=54-3x equation:


Simplifying
2x2 = 54 + -3x

Solving
2x2 = 54 + -3x

Solving for variable 'x'.

Reorder the terms:
-54 + 3x + 2x2 = 54 + -3x + -54 + 3x

Reorder the terms:
-54 + 3x + 2x2 = 54 + -54 + -3x + 3x

Combine like terms: 54 + -54 = 0
-54 + 3x + 2x2 = 0 + -3x + 3x
-54 + 3x + 2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-54 + 3x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(9 + -2x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 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 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5

Solution

x = {-6, 4.5}

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