(x-3)(x+9)=27

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Solution for (x-3)(x+9)=27 equation:


Simplifying
(x + -3)(x + 9) = 27

Reorder the terms:
(-3 + x)(x + 9) = 27

Reorder the terms:
(-3 + x)(9 + x) = 27

Multiply (-3 + x) * (9 + x)
(-3(9 + x) + x(9 + x)) = 27
((9 * -3 + x * -3) + x(9 + x)) = 27
((-27 + -3x) + x(9 + x)) = 27
(-27 + -3x + (9 * x + x * x)) = 27
(-27 + -3x + (9x + x2)) = 27

Combine like terms: -3x + 9x = 6x
(-27 + 6x + x2) = 27

Solving
-27 + 6x + x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + -27 + 6x + x2 = 27 + -27

Combine like terms: -27 + -27 = -54
-54 + 6x + x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-54 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 6x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 6x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 6x + x2 = 0 + 54
6x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
6x + x2 = 54

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 54 + 9

Reorder the terms:
9 + 6x + x2 = 54 + 9

Combine like terms: 54 + 9 = 63
9 + 6x + x2 = 63

Factor a perfect square on the left side:
(x + 3)(x + 3) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + 3) equal to 7.937253933 and -7.937253933.

Subproblem 1

x + 3 = 7.937253933 Simplifying x + 3 = 7.937253933 Reorder the terms: 3 + x = 7.937253933 Solving 3 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.937253933 + -3 x = 7.937253933 + -3 Combine like terms: 7.937253933 + -3 = 4.937253933 x = 4.937253933 Simplifying x = 4.937253933

Subproblem 2

x + 3 = -7.937253933 Simplifying x + 3 = -7.937253933 Reorder the terms: 3 + x = -7.937253933 Solving 3 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.937253933 + -3 x = -7.937253933 + -3 Combine like terms: -7.937253933 + -3 = -10.937253933 x = -10.937253933 Simplifying x = -10.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.937253933, -10.937253933}

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