(x-1)(x-1)+(20-3x-7)(20-3x-7)=50

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Solution for (x-1)(x-1)+(20-3x-7)(20-3x-7)=50 equation:


Simplifying
(x + -1)(x + -1) + (20 + -3x + -7)(20 + -3x + -7) = 50

Reorder the terms:
(-1 + x)(x + -1) + (20 + -3x + -7)(20 + -3x + -7) = 50

Reorder the terms:
(-1 + x)(-1 + x) + (20 + -3x + -7)(20 + -3x + -7) = 50

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) + (20 + -3x + -7)(20 + -3x + -7) = 50
((-1 * -1 + x * -1) + x(-1 + x)) + (20 + -3x + -7)(20 + -3x + -7) = 50
((1 + -1x) + x(-1 + x)) + (20 + -3x + -7)(20 + -3x + -7) = 50
(1 + -1x + (-1 * x + x * x)) + (20 + -3x + -7)(20 + -3x + -7) = 50
(1 + -1x + (-1x + x2)) + (20 + -3x + -7)(20 + -3x + -7) = 50

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) + (20 + -3x + -7)(20 + -3x + -7) = 50

Reorder the terms:
1 + -2x + x2 + (20 + -7 + -3x)(20 + -3x + -7) = 50

Combine like terms: 20 + -7 = 13
1 + -2x + x2 + (13 + -3x)(20 + -3x + -7) = 50

Reorder the terms:
1 + -2x + x2 + (13 + -3x)(20 + -7 + -3x) = 50

Combine like terms: 20 + -7 = 13
1 + -2x + x2 + (13 + -3x)(13 + -3x) = 50

Multiply (13 + -3x) * (13 + -3x)
1 + -2x + x2 + (13(13 + -3x) + -3x * (13 + -3x)) = 50
1 + -2x + x2 + ((13 * 13 + -3x * 13) + -3x * (13 + -3x)) = 50
1 + -2x + x2 + ((169 + -39x) + -3x * (13 + -3x)) = 50
1 + -2x + x2 + (169 + -39x + (13 * -3x + -3x * -3x)) = 50
1 + -2x + x2 + (169 + -39x + (-39x + 9x2)) = 50

Combine like terms: -39x + -39x = -78x
1 + -2x + x2 + (169 + -78x + 9x2) = 50

Reorder the terms:
1 + 169 + -2x + -78x + x2 + 9x2 = 50

Combine like terms: 1 + 169 = 170
170 + -2x + -78x + x2 + 9x2 = 50

Combine like terms: -2x + -78x = -80x
170 + -80x + x2 + 9x2 = 50

Combine like terms: x2 + 9x2 = 10x2
170 + -80x + 10x2 = 50

Solving
170 + -80x + 10x2 = 50

Solving for variable 'x'.

Reorder the terms:
170 + -50 + -80x + 10x2 = 50 + -50

Combine like terms: 170 + -50 = 120
120 + -80x + 10x2 = 50 + -50

Combine like terms: 50 + -50 = 0
120 + -80x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(12 + -8x + x2) = 0

Factor a trinomial.
10((2 + -1x)(6 + -1x)) = 0

Ignore the factor 10.

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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {2, 6}

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