109+x^2-4x+75=180

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Solution for 109+x^2-4x+75=180 equation:


Simplifying
109 + x2 + -4x + 75 = 180

Reorder the terms:
109 + 75 + -4x + x2 = 180

Combine like terms: 109 + 75 = 184
184 + -4x + x2 = 180

Solving
184 + -4x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
184 + -180 + -4x + x2 = 180 + -180

Combine like terms: 184 + -180 = 4
4 + -4x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
4 + -4x + x2 = 0

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

Subproblem 1

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

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 = {2, 2}

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