5x^2+30x+150=1220

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Solution for 5x^2+30x+150=1220 equation:


Simplifying
5x2 + 30x + 150 = 1220

Reorder the terms:
150 + 30x + 5x2 = 1220

Solving
150 + 30x + 5x2 = 1220

Solving for variable 'x'.

Reorder the terms:
150 + -1220 + 30x + 5x2 = 1220 + -1220

Combine like terms: 150 + -1220 = -1070
-1070 + 30x + 5x2 = 1220 + -1220

Combine like terms: 1220 + -1220 = 0
-1070 + 30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-214 + 6x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-214 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-214 + 6x + x2 = 0

Solving
-214 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '214' to each side of the equation.
-214 + 6x + 214 + x2 = 0 + 214

Reorder the terms:
-214 + 214 + 6x + x2 = 0 + 214

Combine like terms: -214 + 214 = 0
0 + 6x + x2 = 0 + 214
6x + x2 = 0 + 214

Combine like terms: 0 + 214 = 214
6x + x2 = 214

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 214 + 9

Reorder the terms:
9 + 6x + x2 = 214 + 9

Combine like terms: 214 + 9 = 223
9 + 6x + x2 = 223

Factor a perfect square on the left side:
(x + 3)(x + 3) = 223

Calculate the square root of the right side: 14.933184523

Break this problem into two subproblems by setting 
(x + 3) equal to 14.933184523 and -14.933184523.


Subproblem 1
x + 3 = 14.933184523

Simplifying
x + 3 = 14.933184523

Reorder the terms:
3 + x = 14.933184523

Solving
3 + x = 14.933184523

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 14.933184523 + -3

Combine like terms: 3 + -3 = 0
0 + x = 14.933184523 + -3
x = 14.933184523 + -3

Combine like terms: 14.933184523 + -3 = 11.933184523
x = 11.933184523

Simplifying
x = 11.933184523


Subproblem 2
x + 3 = -14.933184523

Simplifying
x + 3 = -14.933184523

Reorder the terms:
3 + x = -14.933184523

Solving
3 + x = -14.933184523

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -14.933184523 + -3

Combine like terms: 3 + -3 = 0
0 + x = -14.933184523 + -3
x = -14.933184523 + -3

Combine like terms: -14.933184523 + -3 = -17.933184523
x = -17.933184523

Simplifying
x = -17.933184523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.933184523, -17.933184523}
Solution
x = {11.933184523, -17.933184523}

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