(x)(2x+9)=320

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Solution for (x)(2x+9)=320 equation:


Simplifying
(x)(2x + 9) = 320

Reorder the terms:
x(9 + 2x) = 320
(9 * x + 2x * x) = 320
(9x + 2x2) = 320

Solving
9x + 2x2 = 320

Solving for variable 'x'.

Reorder the terms:
-320 + 9x + 2x2 = 320 + -320

Combine like terms: 320 + -320 = 0
-320 + 9x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-160 + 4.5x + x2 = 0

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 4.5x + 160 + x2 = 0 + 160

Reorder the terms:
-160 + 160 + 4.5x + x2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 4.5x + x2 = 0 + 160
4.5x + x2 = 0 + 160

Combine like terms: 0 + 160 = 160
4.5x + x2 = 160

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 160 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 160 + 5.0625

Combine like terms: 160 + 5.0625 = 165.0625
5.0625 + 4.5x + x2 = 165.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 165.0625

Calculate the square root of the right side: 12.847665158

Break this problem into two subproblems by setting 
(x + 2.25) equal to 12.847665158 and -12.847665158.

Subproblem 1

x + 2.25 = 12.847665158 Simplifying x + 2.25 = 12.847665158 Reorder the terms: 2.25 + x = 12.847665158 Solving 2.25 + x = 12.847665158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 12.847665158 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 12.847665158 + -2.25 x = 12.847665158 + -2.25 Combine like terms: 12.847665158 + -2.25 = 10.597665158 x = 10.597665158 Simplifying x = 10.597665158

Subproblem 2

x + 2.25 = -12.847665158 Simplifying x + 2.25 = -12.847665158 Reorder the terms: 2.25 + x = -12.847665158 Solving 2.25 + x = -12.847665158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -12.847665158 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -12.847665158 + -2.25 x = -12.847665158 + -2.25 Combine like terms: -12.847665158 + -2.25 = -15.097665158 x = -15.097665158 Simplifying x = -15.097665158

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.597665158, -15.097665158}

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