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

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Solution for (x+9)(x-1)=(x+3)2 equation:


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

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

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

Multiply (9 + x) * (-1 + x)
(9(-1 + x) + x(-1 + x)) = (x + 3) * 2
((-1 * 9 + x * 9) + x(-1 + x)) = (x + 3) * 2
((-9 + 9x) + x(-1 + x)) = (x + 3) * 2
(-9 + 9x + (-1 * x + x * x)) = (x + 3) * 2
(-9 + 9x + (-1x + x2)) = (x + 3) * 2

Combine like terms: 9x + -1x = 8x
(-9 + 8x + x2) = (x + 3) * 2

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

Reorder the terms for easier multiplication:
-9 + 8x + x2 = 2(3 + x)
-9 + 8x + x2 = (3 * 2 + x * 2)
-9 + 8x + x2 = (6 + 2x)

Solving
-9 + 8x + x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
-9 + -6 + 8x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: -9 + -6 = -15
-15 + 8x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 8x + -2x = 6x
-15 + 6x + x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-15 + 6x + x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-15 + 6x + x2 = 0 + 2x + -2x
-15 + 6x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-15 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 6x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 6x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 6x + x2 = 0 + 15
6x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
6x + x2 = 15

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 = 15 + 9

Reorder the terms:
9 + 6x + x2 = 15 + 9

Combine like terms: 15 + 9 = 24
9 + 6x + x2 = 24

Factor a perfect square on the left side:
(x + 3)(x + 3) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 3) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + 3 = 4.898979486 Simplifying x + 3 = 4.898979486 Reorder the terms: 3 + x = 4.898979486 Solving 3 + x = 4.898979486 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 = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.898979486 + -3 x = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 x = 1.898979486 Simplifying x = 1.898979486

Subproblem 2

x + 3 = -4.898979486 Simplifying x + 3 = -4.898979486 Reorder the terms: 3 + x = -4.898979486 Solving 3 + x = -4.898979486 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 = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.898979486 + -3 x = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 x = -7.898979486 Simplifying x = -7.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.898979486, -7.898979486}

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