(2x-9)(2x-9)=49

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Solution for (2x-9)(2x-9)=49 equation: 


Simplifying
(2x + -9)(2x + -9) = 49

Reorder the terms:
(-9 + 2x)(2x + -9) = 49

Reorder the terms:
(-9 + 2x)(-9 + 2x) = 49

Multiply (-9 + 2x) * (-9 + 2x)
(-9(-9 + 2x) + 2x * (-9 + 2x)) = 49
((-9 * -9 + 2x * -9) + 2x * (-9 + 2x)) = 49
((81 + -18x) + 2x * (-9 + 2x)) = 49
(81 + -18x + (-9 * 2x + 2x * 2x)) = 49
(81 + -18x + (-18x + 4x2)) = 49

Combine like terms: -18x + -18x = -36x
(81 + -36x + 4x2) = 49

Solving
81 + -36x + 4x2 = 49

Solving for variable 'x'.

Reorder the terms:
81 + -49 + -36x + 4x2 = 49 + -49

Combine like terms: 81 + -49 = 32
32 + -36x + 4x2 = 49 + -49

Combine like terms: 49 + -49 = 0
32 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -9x + x2) = 0

Factor a trinomial.
4((1 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {1, 8}

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