(x+6)(x-9)=6

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Solution for (x+6)(x-9)=6 equation:


Simplifying
(x + 6)(x + -9) = 6

Reorder the terms:
(6 + x)(x + -9) = 6

Reorder the terms:
(6 + x)(-9 + x) = 6

Multiply (6 + x) * (-9 + x)
(6(-9 + x) + x(-9 + x)) = 6
((-9 * 6 + x * 6) + x(-9 + x)) = 6
((-54 + 6x) + x(-9 + x)) = 6
(-54 + 6x + (-9 * x + x * x)) = 6
(-54 + 6x + (-9x + x2)) = 6

Combine like terms: 6x + -9x = -3x
(-54 + -3x + x2) = 6

Solving
-54 + -3x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-54 + -6 + -3x + x2 = 6 + -6

Combine like terms: -54 + -6 = -60
-60 + -3x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-60 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -3x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -3x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -3x + x2 = 0 + 60
-3x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-3x + x2 = 60

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 = 60 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 60 + 2.25

Combine like terms: 60 + 2.25 = 62.25
2.25 + -3x + x2 = 62.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + -1.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

x + -1.5 = 7.889866919 Simplifying x + -1.5 = 7.889866919 Reorder the terms: -1.5 + x = 7.889866919 Solving -1.5 + x = 7.889866919 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 = 7.889866919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.889866919 + 1.5 x = 7.889866919 + 1.5 Combine like terms: 7.889866919 + 1.5 = 9.389866919 x = 9.389866919 Simplifying x = 9.389866919

Subproblem 2

x + -1.5 = -7.889866919 Simplifying x + -1.5 = -7.889866919 Reorder the terms: -1.5 + x = -7.889866919 Solving -1.5 + x = -7.889866919 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 = -7.889866919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.889866919 + 1.5 x = -7.889866919 + 1.5 Combine like terms: -7.889866919 + 1.5 = -6.389866919 x = -6.389866919 Simplifying x = -6.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.389866919, -6.389866919}

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