2x(x-4)-9=4(3-x)

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Solution for 2x(x-4)-9=4(3-x) equation:


Simplifying
2x(x + -4) + -9 = 4(3 + -1x)

Reorder the terms:
2x(-4 + x) + -9 = 4(3 + -1x)
(-4 * 2x + x * 2x) + -9 = 4(3 + -1x)
(-8x + 2x2) + -9 = 4(3 + -1x)

Reorder the terms:
-9 + -8x + 2x2 = 4(3 + -1x)
-9 + -8x + 2x2 = (3 * 4 + -1x * 4)
-9 + -8x + 2x2 = (12 + -4x)

Solving
-9 + -8x + 2x2 = 12 + -4x

Solving for variable 'x'.

Reorder the terms:
-9 + -12 + -8x + 4x + 2x2 = 12 + -4x + -12 + 4x

Combine like terms: -9 + -12 = -21
-21 + -8x + 4x + 2x2 = 12 + -4x + -12 + 4x

Combine like terms: -8x + 4x = -4x
-21 + -4x + 2x2 = 12 + -4x + -12 + 4x

Reorder the terms:
-21 + -4x + 2x2 = 12 + -12 + -4x + 4x

Combine like terms: 12 + -12 = 0
-21 + -4x + 2x2 = 0 + -4x + 4x
-21 + -4x + 2x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-21 + -4x + 2x2 = 0

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

Divide each side by '2'.
-10.5 + -2x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -2x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -2x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -2x + x2 = 0 + 10.5
-2x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-2x + x2 = 10.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 10.5 + 1

Reorder the terms:
1 + -2x + x2 = 10.5 + 1

Combine like terms: 10.5 + 1 = 11.5
1 + -2x + x2 = 11.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(x + -1) equal to 3.391164992 and -3.391164992.

Subproblem 1

x + -1 = 3.391164992 Simplifying x + -1 = 3.391164992 Reorder the terms: -1 + x = 3.391164992 Solving -1 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.391164992 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.391164992 + 1 x = 3.391164992 + 1 Combine like terms: 3.391164992 + 1 = 4.391164992 x = 4.391164992 Simplifying x = 4.391164992

Subproblem 2

x + -1 = -3.391164992 Simplifying x + -1 = -3.391164992 Reorder the terms: -1 + x = -3.391164992 Solving -1 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.391164992 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.391164992 + 1 x = -3.391164992 + 1 Combine like terms: -3.391164992 + 1 = -2.391164992 x = -2.391164992 Simplifying x = -2.391164992

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.391164992, -2.391164992}

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