(2x-11)(2x-11)-16(4x-10)=38-5*x*x

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Solution for (2x-11)(2x-11)-16(4x-10)=38-5*x*x equation: 


Simplifying
(2x + -11)(2x + -11) + -16(4x + -10) = 38 + -5x * x

Reorder the terms:
(-11 + 2x)(2x + -11) + -16(4x + -10) = 38 + -5x * x

Reorder the terms:
(-11 + 2x)(-11 + 2x) + -16(4x + -10) = 38 + -5x * x

Multiply (-11 + 2x) * (-11 + 2x)
(-11(-11 + 2x) + 2x * (-11 + 2x)) + -16(4x + -10) = 38 + -5x * x
((-11 * -11 + 2x * -11) + 2x * (-11 + 2x)) + -16(4x + -10) = 38 + -5x * x
((121 + -22x) + 2x * (-11 + 2x)) + -16(4x + -10) = 38 + -5x * x
(121 + -22x + (-11 * 2x + 2x * 2x)) + -16(4x + -10) = 38 + -5x * x
(121 + -22x + (-22x + 4x2)) + -16(4x + -10) = 38 + -5x * x

Combine like terms: -22x + -22x = -44x
(121 + -44x + 4x2) + -16(4x + -10) = 38 + -5x * x

Reorder the terms:
121 + -44x + 4x2 + -16(-10 + 4x) = 38 + -5x * x
121 + -44x + 4x2 + (-10 * -16 + 4x * -16) = 38 + -5x * x
121 + -44x + 4x2 + (160 + -64x) = 38 + -5x * x

Reorder the terms:
121 + 160 + -44x + -64x + 4x2 = 38 + -5x * x

Combine like terms: 121 + 160 = 281
281 + -44x + -64x + 4x2 = 38 + -5x * x

Combine like terms: -44x + -64x = -108x
281 + -108x + 4x2 = 38 + -5x * x

Multiply x * x
281 + -108x + 4x2 = 38 + -5x2

Solving
281 + -108x + 4x2 = 38 + -5x2

Solving for variable 'x'.

Reorder the terms:
281 + -38 + -108x + 4x2 + 5x2 = 38 + -5x2 + -38 + 5x2

Combine like terms: 281 + -38 = 243
243 + -108x + 4x2 + 5x2 = 38 + -5x2 + -38 + 5x2

Combine like terms: 4x2 + 5x2 = 9x2
243 + -108x + 9x2 = 38 + -5x2 + -38 + 5x2

Reorder the terms:
243 + -108x + 9x2 = 38 + -38 + -5x2 + 5x2

Combine like terms: 38 + -38 = 0
243 + -108x + 9x2 = 0 + -5x2 + 5x2
243 + -108x + 9x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
243 + -108x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(27 + -12x + x2) = 0

Factor a trinomial.
9((3 + -1x)(9 + -1x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {3, 9}

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