0=(8.5-2x)(11-2x)

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Solution for 0=(8.5-2x)(11-2x) equation:


Simplifying
0 = (8.5 + -2x)(11 + -2x)

Multiply (8.5 + -2x) * (11 + -2x)
0 = (8.5(11 + -2x) + -2x * (11 + -2x))
0 = ((11 * 8.5 + -2x * 8.5) + -2x * (11 + -2x))
0 = ((93.5 + -17x) + -2x * (11 + -2x))
0 = (93.5 + -17x + (11 * -2x + -2x * -2x))
0 = (93.5 + -17x + (-22x + 4x2))

Combine like terms: -17x + -22x = -39x
0 = (93.5 + -39x + 4x2)

Solving
0 = 93.5 + -39x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -93.5 = -93.5
-93.5 + 39x + -4x2 = 93.5 + -39x + 4x2 + -93.5 + 39x + -4x2

Reorder the terms:
-93.5 + 39x + -4x2 = 93.5 + -93.5 + -39x + 39x + 4x2 + -4x2

Combine like terms: 93.5 + -93.5 = 0.0
-93.5 + 39x + -4x2 = 0.0 + -39x + 39x + 4x2 + -4x2
-93.5 + 39x + -4x2 = -39x + 39x + 4x2 + -4x2

Combine like terms: -39x + 39x = 0
-93.5 + 39x + -4x2 = 0 + 4x2 + -4x2
-93.5 + 39x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-93.5 + 39x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
23.375 + -9.75x + x2 = 0

Move the constant term to the right:

Add '-23.375' to each side of the equation.
23.375 + -9.75x + -23.375 + x2 = 0 + -23.375

Reorder the terms:
23.375 + -23.375 + -9.75x + x2 = 0 + -23.375

Combine like terms: 23.375 + -23.375 = 0.000
0.000 + -9.75x + x2 = 0 + -23.375
-9.75x + x2 = 0 + -23.375

Combine like terms: 0 + -23.375 = -23.375
-9.75x + x2 = -23.375

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = -23.375 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = -23.375 + 23.765625

Combine like terms: -23.375 + 23.765625 = 0.390625
23.765625 + -9.75x + x2 = 0.390625

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 0.390625

Calculate the square root of the right side: 0.625

Break this problem into two subproblems by setting 
(x + -4.875) equal to 0.625 and -0.625.

Subproblem 1

x + -4.875 = 0.625 Simplifying x + -4.875 = 0.625 Reorder the terms: -4.875 + x = 0.625 Solving -4.875 + x = 0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 0.625 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 0.625 + 4.875 x = 0.625 + 4.875 Combine like terms: 0.625 + 4.875 = 5.5 x = 5.5 Simplifying x = 5.5

Subproblem 2

x + -4.875 = -0.625 Simplifying x + -4.875 = -0.625 Reorder the terms: -4.875 + x = -0.625 Solving -4.875 + x = -0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -0.625 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -0.625 + 4.875 x = -0.625 + 4.875 Combine like terms: -0.625 + 4.875 = 4.25 x = 4.25 Simplifying x = 4.25

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.5, 4.25}

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