(x-5)2=x(x-8)+11

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Solution for (x-5)2=x(x-8)+11 equation:


Simplifying
(x + -5) * 2 = x(x + -8) + 11

Reorder the terms:
(-5 + x) * 2 = x(x + -8) + 11

Reorder the terms for easier multiplication:
2(-5 + x) = x(x + -8) + 11
(-5 * 2 + x * 2) = x(x + -8) + 11
(-10 + 2x) = x(x + -8) + 11

Reorder the terms:
-10 + 2x = x(-8 + x) + 11
-10 + 2x = (-8 * x + x * x) + 11
-10 + 2x = (-8x + x2) + 11

Reorder the terms:
-10 + 2x = 11 + -8x + x2

Solving
-10 + 2x = 11 + -8x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + -11 + 2x + 8x + -1x2 = 11 + -8x + x2 + -11 + 8x + -1x2

Combine like terms: -10 + -11 = -21
-21 + 2x + 8x + -1x2 = 11 + -8x + x2 + -11 + 8x + -1x2

Combine like terms: 2x + 8x = 10x
-21 + 10x + -1x2 = 11 + -8x + x2 + -11 + 8x + -1x2

Reorder the terms:
-21 + 10x + -1x2 = 11 + -11 + -8x + 8x + x2 + -1x2

Combine like terms: 11 + -11 = 0
-21 + 10x + -1x2 = 0 + -8x + 8x + x2 + -1x2
-21 + 10x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-21 + 10x + -1x2 = 0 + x2 + -1x2
-21 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 10x + -1x2 = 0

Factor a trinomial.
(-7 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 2
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
Solution
x = {7, 3}

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