5x^2+80x+285=0

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Solution for 5x^2+80x+285=0 equation: 


Simplifying
5x2 + 80x + 285 = 0

Reorder the terms:
285 + 80x + 5x2 = 0

Solving
285 + 80x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(57 + 16x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(57 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
57 + 16x + x2 = 0

Solving
57 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-57' to each side of the equation.
57 + 16x + -57 + x2 = 0 + -57

Reorder the terms:
57 + -57 + 16x + x2 = 0 + -57

Combine like terms: 57 + -57 = 0
0 + 16x + x2 = 0 + -57
16x + x2 = 0 + -57

Combine like terms: 0 + -57 = -57
16x + x2 = -57

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -57 + 64

Reorder the terms:
64 + 16x + x2 = -57 + 64

Combine like terms: -57 + 64 = 7
64 + 16x + x2 = 7

Factor a perfect square on the left side:
(x + 8)(x + 8) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 8) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + 8 = 2.645751311

Simplifying
x + 8 = 2.645751311

Reorder the terms:
8 + x = 2.645751311

Solving
8 + x = 2.645751311

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = 2.645751311 + -8

Combine like terms: 8 + -8 = 0
0 + x = 2.645751311 + -8
x = 2.645751311 + -8

Combine like terms: 2.645751311 + -8 = -5.354248689
x = -5.354248689

Simplifying
x = -5.354248689


Subproblem 2
x + 8 = -2.645751311

Simplifying
x + 8 = -2.645751311

Reorder the terms:
8 + x = -2.645751311

Solving
8 + x = -2.645751311

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = -2.645751311 + -8

Combine like terms: 8 + -8 = 0
0 + x = -2.645751311 + -8
x = -2.645751311 + -8

Combine like terms: -2.645751311 + -8 = -10.645751311
x = -10.645751311

Simplifying
x = -10.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.354248689, -10.645751311}
Solution
x = {-5.354248689, -10.645751311}

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