(x+4)(x-12)=-5x

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Solution for (x+4)(x-12)=-5x equation:


Simplifying
(x + 4)(x + -12) = -5x

Reorder the terms:
(4 + x)(x + -12) = -5x

Reorder the terms:
(4 + x)(-12 + x) = -5x

Multiply (4 + x) * (-12 + x)
(4(-12 + x) + x(-12 + x)) = -5x
((-12 * 4 + x * 4) + x(-12 + x)) = -5x
((-48 + 4x) + x(-12 + x)) = -5x
(-48 + 4x + (-12 * x + x * x)) = -5x
(-48 + 4x + (-12x + x2)) = -5x

Combine like terms: 4x + -12x = -8x
(-48 + -8x + x2) = -5x

Solving
-48 + -8x + x2 = -5x

Solving for variable 'x'.

Reorder the terms:
-48 + -8x + 5x + x2 = -5x + 5x

Combine like terms: -8x + 5x = -3x
-48 + -3x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-48 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -3x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -3x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -3x + x2 = 0 + 48
-3x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-3x + x2 = 48

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 48 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 48 + 2.25

Combine like terms: 48 + 2.25 = 50.25
2.25 + -3x + x2 = 50.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + -1.5) equal to 7.088723439 and -7.088723439.

Subproblem 1

x + -1.5 = 7.088723439 Simplifying x + -1.5 = 7.088723439 Reorder the terms: -1.5 + x = 7.088723439 Solving -1.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.088723439 + 1.5 x = 7.088723439 + 1.5 Combine like terms: 7.088723439 + 1.5 = 8.588723439 x = 8.588723439 Simplifying x = 8.588723439

Subproblem 2

x + -1.5 = -7.088723439 Simplifying x + -1.5 = -7.088723439 Reorder the terms: -1.5 + x = -7.088723439 Solving -1.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.088723439 + 1.5 x = -7.088723439 + 1.5 Combine like terms: -7.088723439 + 1.5 = -5.588723439 x = -5.588723439 Simplifying x = -5.588723439

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.588723439, -5.588723439}

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