(5-2x)(2-x)=22-8x

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Solution for (5-2x)(2-x)=22-8x equation:


Simplifying
(5 + -2x)(2 + -1x) = 22 + -8x

Multiply (5 + -2x) * (2 + -1x)
(5(2 + -1x) + -2x * (2 + -1x)) = 22 + -8x
((2 * 5 + -1x * 5) + -2x * (2 + -1x)) = 22 + -8x
((10 + -5x) + -2x * (2 + -1x)) = 22 + -8x
(10 + -5x + (2 * -2x + -1x * -2x)) = 22 + -8x
(10 + -5x + (-4x + 2x2)) = 22 + -8x

Combine like terms: -5x + -4x = -9x
(10 + -9x + 2x2) = 22 + -8x

Solving
10 + -9x + 2x2 = 22 + -8x

Solving for variable 'x'.

Reorder the terms:
10 + -22 + -9x + 8x + 2x2 = 22 + -8x + -22 + 8x

Combine like terms: 10 + -22 = -12
-12 + -9x + 8x + 2x2 = 22 + -8x + -22 + 8x

Combine like terms: -9x + 8x = -1x
-12 + -1x + 2x2 = 22 + -8x + -22 + 8x

Reorder the terms:
-12 + -1x + 2x2 = 22 + -22 + -8x + 8x

Combine like terms: 22 + -22 = 0
-12 + -1x + 2x2 = 0 + -8x + 8x
-12 + -1x + 2x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-12 + -1x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-6 + -0.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -0.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -0.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -0.5x + x2 = 0 + 6
-0.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-0.5x + x2 = 6

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 6 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 6 + 0.0625

Combine like terms: 6 + 0.0625 = 6.0625
0.0625 + -0.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.46221445 and -2.46221445.

Subproblem 1

x + -0.25 = 2.46221445 Simplifying x + -0.25 = 2.46221445 Reorder the terms: -0.25 + x = 2.46221445 Solving -0.25 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.46221445 + 0.25 x = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 x = 2.71221445 Simplifying x = 2.71221445

Subproblem 2

x + -0.25 = -2.46221445 Simplifying x + -0.25 = -2.46221445 Reorder the terms: -0.25 + x = -2.46221445 Solving -0.25 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.46221445 + 0.25 x = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 x = -2.21221445 Simplifying x = -2.21221445

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.71221445, -2.21221445}

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