x^2+9x-380=0

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Solution for x^2+9x-380=0 equation:


Simplifying
x2 + 9x + -380 = 0

Reorder the terms:
-380 + 9x + x2 = 0

Solving
-380 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '380' to each side of the equation.
-380 + 9x + 380 + x2 = 0 + 380

Reorder the terms:
-380 + 380 + 9x + x2 = 0 + 380

Combine like terms: -380 + 380 = 0
0 + 9x + x2 = 0 + 380
9x + x2 = 0 + 380

Combine like terms: 0 + 380 = 380
9x + x2 = 380

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 = 380 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 380 + 20.25

Combine like terms: 380 + 20.25 = 400.25
20.25 + 9x + x2 = 400.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 400.25

Calculate the square root of the right side: 20.006249024

Break this problem into two subproblems by setting 
(x + 4.5) equal to 20.006249024 and -20.006249024.

Subproblem 1

x + 4.5 = 20.006249024 Simplifying x + 4.5 = 20.006249024 Reorder the terms: 4.5 + x = 20.006249024 Solving 4.5 + x = 20.006249024 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 = 20.006249024 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 20.006249024 + -4.5 x = 20.006249024 + -4.5 Combine like terms: 20.006249024 + -4.5 = 15.506249024 x = 15.506249024 Simplifying x = 15.506249024

Subproblem 2

x + 4.5 = -20.006249024 Simplifying x + 4.5 = -20.006249024 Reorder the terms: 4.5 + x = -20.006249024 Solving 4.5 + x = -20.006249024 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 = -20.006249024 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -20.006249024 + -4.5 x = -20.006249024 + -4.5 Combine like terms: -20.006249024 + -4.5 = -24.506249024 x = -24.506249024 Simplifying x = -24.506249024

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.506249024, -24.506249024}

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