x^2+9x=328

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Solution for x^2+9x=328 equation:


Simplifying
x2 + 9x = 328

Reorder the terms:
9x + x2 = 328

Solving
9x + x2 = 328

Solving for variable 'x'.

Reorder the terms:
-328 + 9x + x2 = 328 + -328

Combine like terms: 328 + -328 = 0
-328 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '328' to each side of the equation.
-328 + 9x + 328 + x2 = 0 + 328

Reorder the terms:
-328 + 328 + 9x + x2 = 0 + 328

Combine like terms: -328 + 328 = 0
0 + 9x + x2 = 0 + 328
9x + x2 = 0 + 328

Combine like terms: 0 + 328 = 328
9x + x2 = 328

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 328 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 328 + 20.25

Combine like terms: 328 + 20.25 = 348.25
20.25 + 9x + x2 = 348.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 348.25

Calculate the square root of the right side: 18.661457607

Break this problem into two subproblems by setting 
(x + 4.5) equal to 18.661457607 and -18.661457607.

Subproblem 1

x + 4.5 = 18.661457607 Simplifying x + 4.5 = 18.661457607 Reorder the terms: 4.5 + x = 18.661457607 Solving 4.5 + x = 18.661457607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 18.661457607 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 18.661457607 + -4.5 x = 18.661457607 + -4.5 Combine like terms: 18.661457607 + -4.5 = 14.161457607 x = 14.161457607 Simplifying x = 14.161457607

Subproblem 2

x + 4.5 = -18.661457607 Simplifying x + 4.5 = -18.661457607 Reorder the terms: 4.5 + x = -18.661457607 Solving 4.5 + x = -18.661457607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -18.661457607 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -18.661457607 + -4.5 x = -18.661457607 + -4.5 Combine like terms: -18.661457607 + -4.5 = -23.161457607 x = -23.161457607 Simplifying x = -23.161457607

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.161457607, -23.161457607}

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