0=x^2-22x+40

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Solution for 0=x^2-22x+40 equation:


Simplifying
0 = x2 + -22x + 40

Reorder the terms:
0 = 40 + -22x + x2

Solving
0 = 40 + -22x + x2

Solving for variable 'x'.

Combine like terms: 0 + -40 = -40
-40 + 22x + -1x2 = 40 + -22x + x2 + -40 + 22x + -1x2

Reorder the terms:
-40 + 22x + -1x2 = 40 + -40 + -22x + 22x + x2 + -1x2

Combine like terms: 40 + -40 = 0
-40 + 22x + -1x2 = 0 + -22x + 22x + x2 + -1x2
-40 + 22x + -1x2 = -22x + 22x + x2 + -1x2

Combine like terms: -22x + 22x = 0
-40 + 22x + -1x2 = 0 + x2 + -1x2
-40 + 22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + 22x + -1x2 = 0

Factor a trinomial.
(-20 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-20 + x)' equal to zero and attempt to solve: Simplifying -20 + x = 0 Solving -20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Simplifying x = 20

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 = {20, 2}

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