2*(x-3)(x-3)+18=26

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Solution for 2*(x-3)(x-3)+18=26 equation:


Simplifying
2(x + -3)(x + -3) + 18 = 26

Reorder the terms:
2(-3 + x)(x + -3) + 18 = 26

Reorder the terms:
2(-3 + x)(-3 + x) + 18 = 26

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) + 18 = 26
2((-3 * -3 + x * -3) + x(-3 + x)) + 18 = 26
2((9 + -3x) + x(-3 + x)) + 18 = 26
2(9 + -3x + (-3 * x + x * x)) + 18 = 26
2(9 + -3x + (-3x + x2)) + 18 = 26

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) + 18 = 26
(9 * 2 + -6x * 2 + x2 * 2) + 18 = 26
(18 + -12x + 2x2) + 18 = 26

Reorder the terms:
18 + 18 + -12x + 2x2 = 26

Combine like terms: 18 + 18 = 36
36 + -12x + 2x2 = 26

Solving
36 + -12x + 2x2 = 26

Solving for variable 'x'.

Reorder the terms:
36 + -26 + -12x + 2x2 = 26 + -26

Combine like terms: 36 + -26 = 10
10 + -12x + 2x2 = 26 + -26

Combine like terms: 26 + -26 = 0
10 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6x + x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

x = {1, 5}

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