10x^2+45x=25

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Solution for 10x^2+45x=25 equation:


Simplifying
10x2 + 45x = 25

Reorder the terms:
45x + 10x2 = 25

Solving
45x + 10x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 45x + 10x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 45x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 9x + 2x2) = 0

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

Ignore the factor 5.

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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-5, 0.5}

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