(x+3)(x-3)=16-2x

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Solution for (x+3)(x-3)=16-2x equation:


Simplifying
(x + 3)(x + -3) = 16 + -2x

Reorder the terms:
(3 + x)(x + -3) = 16 + -2x

Reorder the terms:
(3 + x)(-3 + x) = 16 + -2x

Multiply (3 + x) * (-3 + x)
(3(-3 + x) + x(-3 + x)) = 16 + -2x
((-3 * 3 + x * 3) + x(-3 + x)) = 16 + -2x
((-9 + 3x) + x(-3 + x)) = 16 + -2x
(-9 + 3x + (-3 * x + x * x)) = 16 + -2x
(-9 + 3x + (-3x + x2)) = 16 + -2x

Combine like terms: 3x + -3x = 0
(-9 + 0 + x2) = 16 + -2x
(-9 + x2) = 16 + -2x

Solving
-9 + x2 = 16 + -2x

Solving for variable 'x'.

Reorder the terms:
-9 + -16 + 2x + x2 = 16 + -2x + -16 + 2x

Combine like terms: -9 + -16 = -25
-25 + 2x + x2 = 16 + -2x + -16 + 2x

Reorder the terms:
-25 + 2x + x2 = 16 + -16 + -2x + 2x

Combine like terms: 16 + -16 = 0
-25 + 2x + x2 = 0 + -2x + 2x
-25 + 2x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-25 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 2x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 2x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2x + x2 = 0 + 25
2x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
2x + x2 = 25

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 = 25 + 1

Reorder the terms:
1 + 2x + x2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + 2x + x2 = 26

Factor a perfect square on the left side:
(x + 1)(x + 1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 1) equal to 5.099019514 and -5.099019514.

Subproblem 1

x + 1 = 5.099019514 Simplifying x + 1 = 5.099019514 Reorder the terms: 1 + x = 5.099019514 Solving 1 + x = 5.099019514 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 = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.099019514 + -1 x = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 x = 4.099019514 Simplifying x = 4.099019514

Subproblem 2

x + 1 = -5.099019514 Simplifying x + 1 = -5.099019514 Reorder the terms: 1 + x = -5.099019514 Solving 1 + x = -5.099019514 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 = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.099019514 + -1 x = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 x = -6.099019514 Simplifying x = -6.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.099019514, -6.099019514}

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