20x^2=10+46x

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Solution for 20x^2=10+46x equation:


Simplifying
20x2 = 10 + 46x

Solving
20x2 = 10 + 46x

Solving for variable 'x'.

Reorder the terms:
-10 + -46x + 20x2 = 10 + 46x + -10 + -46x

Reorder the terms:
-10 + -46x + 20x2 = 10 + -10 + 46x + -46x

Combine like terms: 10 + -10 = 0
-10 + -46x + 20x2 = 0 + 46x + -46x
-10 + -46x + 20x2 = 46x + -46x

Combine like terms: 46x + -46x = 0
-10 + -46x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -23x + 10x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2

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 = {-0.2, 2.5}

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