2x^2+7x=2x+25

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Solution for 2x^2+7x=2x+25 equation:


Simplifying
2x2 + 7x = 2x + 25

Reorder the terms:
7x + 2x2 = 2x + 25

Reorder the terms:
7x + 2x2 = 25 + 2x

Solving
7x + 2x2 = 25 + 2x

Solving for variable 'x'.

Reorder the terms:
-25 + 7x + -2x + 2x2 = 25 + 2x + -25 + -2x

Combine like terms: 7x + -2x = 5x
-25 + 5x + 2x2 = 25 + 2x + -25 + -2x

Reorder the terms:
-25 + 5x + 2x2 = 25 + -25 + 2x + -2x

Combine like terms: 25 + -25 = 0
-25 + 5x + 2x2 = 0 + 2x + -2x
-25 + 5x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-25 + 5x + 2x2 = 0

Factor a trinomial.
(-5 + -1x)(5 + -2x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-5, 2.5}

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