(x-3)(x+5)-9=9

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Solution for (x-3)(x+5)-9=9 equation:


Simplifying
(x + -3)(x + 5) + -9 = 9

Reorder the terms:
(-3 + x)(x + 5) + -9 = 9

Reorder the terms:
(-3 + x)(5 + x) + -9 = 9

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x)) + -9 = 9
((5 * -3 + x * -3) + x(5 + x)) + -9 = 9
((-15 + -3x) + x(5 + x)) + -9 = 9
(-15 + -3x + (5 * x + x * x)) + -9 = 9
(-15 + -3x + (5x + x2)) + -9 = 9

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2) + -9 = 9

Reorder the terms:
-15 + -9 + 2x + x2 = 9

Combine like terms: -15 + -9 = -24
-24 + 2x + x2 = 9

Solving
-24 + 2x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-24 + -9 + 2x + x2 = 9 + -9

Combine like terms: -24 + -9 = -33
-33 + 2x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-33 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 2x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + 2x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 2x + x2 = 0 + 33
2x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
2x + x2 = 33

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 = 33 + 1

Reorder the terms:
1 + 2x + x2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + 2x + x2 = 34

Factor a perfect square on the left side:
(x + 1)(x + 1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + 1) equal to 5.830951895 and -5.830951895.

Subproblem 1

x + 1 = 5.830951895 Simplifying x + 1 = 5.830951895 Reorder the terms: 1 + x = 5.830951895 Solving 1 + x = 5.830951895 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 = 5.830951895 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.830951895 + -1 x = 5.830951895 + -1 Combine like terms: 5.830951895 + -1 = 4.830951895 x = 4.830951895 Simplifying x = 4.830951895

Subproblem 2

x + 1 = -5.830951895 Simplifying x + 1 = -5.830951895 Reorder the terms: 1 + x = -5.830951895 Solving 1 + x = -5.830951895 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 = -5.830951895 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.830951895 + -1 x = -5.830951895 + -1 Combine like terms: -5.830951895 + -1 = -6.830951895 x = -6.830951895 Simplifying x = -6.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.830951895, -6.830951895}

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