(9-2x)(5-2x)=24

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Solution for (9-2x)(5-2x)=24 equation:


Simplifying
(9 + -2x)(5 + -2x) = 24

Multiply (9 + -2x) * (5 + -2x)
(9(5 + -2x) + -2x * (5 + -2x)) = 24
((5 * 9 + -2x * 9) + -2x * (5 + -2x)) = 24
((45 + -18x) + -2x * (5 + -2x)) = 24
(45 + -18x + (5 * -2x + -2x * -2x)) = 24
(45 + -18x + (-10x + 4x2)) = 24

Combine like terms: -18x + -10x = -28x
(45 + -28x + 4x2) = 24

Solving
45 + -28x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
45 + -24 + -28x + 4x2 = 24 + -24

Combine like terms: 45 + -24 = 21
21 + -28x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
21 + -28x + 4x2 = 0

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

Divide each side by '4'.
5.25 + -7x + x2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -7x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -7x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -7x + x2 = 0 + -5.25
-7x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-7x + x2 = -5.25

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -5.25 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -5.25 + 12.25

Combine like terms: -5.25 + 12.25 = 7
12.25 + -7x + x2 = 7

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -3.5 = 2.645751311 Simplifying x + -3.5 = 2.645751311 Reorder the terms: -3.5 + x = 2.645751311 Solving -3.5 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.645751311 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.645751311 + 3.5 x = 2.645751311 + 3.5 Combine like terms: 2.645751311 + 3.5 = 6.145751311 x = 6.145751311 Simplifying x = 6.145751311

Subproblem 2

x + -3.5 = -2.645751311 Simplifying x + -3.5 = -2.645751311 Reorder the terms: -3.5 + x = -2.645751311 Solving -3.5 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.645751311 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.645751311 + 3.5 x = -2.645751311 + 3.5 Combine like terms: -2.645751311 + 3.5 = 0.854248689 x = 0.854248689 Simplifying x = 0.854248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.145751311, 0.854248689}

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