2x^2=100-46x

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Solution for 2x^2=100-46x equation:


Simplifying
2x2 = 100 + -46x

Solving
2x2 = 100 + -46x

Solving for variable 'x'.

Reorder the terms:
-100 + 46x + 2x2 = 100 + -46x + -100 + 46x

Reorder the terms:
-100 + 46x + 2x2 = 100 + -100 + -46x + 46x

Combine like terms: 100 + -100 = 0
-100 + 46x + 2x2 = 0 + -46x + 46x
-100 + 46x + 2x2 = -46x + 46x

Combine like terms: -46x + 46x = 0
-100 + 46x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 23x + x2) = 0

Factor a trinomial.
2((-25 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-25 + -1x)' equal to zero and attempt to solve: Simplifying -25 + -1x = 0 Solving -25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1x = 0 + 25 -1x = 0 + 25 Combine like terms: 0 + 25 = 25 -1x = 25 Divide each side by '-1'. x = -25 Simplifying x = -25

Subproblem 2

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

Solution

x = {-25, 2}

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