2x^2-20x=x^2-100

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Solution for 2x^2-20x=x^2-100 equation:


Simplifying
2x2 + -20x = x2 + -100

Reorder the terms:
-20x + 2x2 = x2 + -100

Reorder the terms:
-20x + 2x2 = -100 + x2

Solving
-20x + 2x2 = -100 + x2

Solving for variable 'x'.

Reorder the terms:
100 + -20x + 2x2 + -1x2 = -100 + x2 + 100 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
100 + -20x + 1x2 = -100 + x2 + 100 + -1x2

Reorder the terms:
100 + -20x + 1x2 = -100 + 100 + x2 + -1x2

Combine like terms: -100 + 100 = 0
100 + -20x + 1x2 = 0 + x2 + -1x2
100 + -20x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
100 + -20x + 1x2 = 0

Factor a trinomial.
(10 + -1x)(10 + -1x) = 0

Subproblem 1

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {10, 10}

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