x^2+30x+10=0

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Solution for x^2+30x+10=0 equation:


Simplifying
x2 + 30x + 10 = 0

Reorder the terms:
10 + 30x + x2 = 0

Solving
10 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 30x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 30x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 30x + x2 = 0 + -10
30x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
30x + x2 = -10

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -10 + 225

Reorder the terms:
225 + 30x + x2 = -10 + 225

Combine like terms: -10 + 225 = 215
225 + 30x + x2 = 215

Factor a perfect square on the left side:
(x + 15)(x + 15) = 215

Calculate the square root of the right side: 14.662878299

Break this problem into two subproblems by setting 
(x + 15) equal to 14.662878299 and -14.662878299.


Subproblem 1
x + 15 = 14.662878299

Simplifying
x + 15 = 14.662878299

Reorder the terms:
15 + x = 14.662878299

Solving
15 + x = 14.662878299

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 14.662878299 + -15

Combine like terms: 15 + -15 = 0
0 + x = 14.662878299 + -15
x = 14.662878299 + -15

Combine like terms: 14.662878299 + -15 = -0.337121701
x = -0.337121701

Simplifying
x = -0.337121701


Subproblem 2
x + 15 = -14.662878299

Simplifying
x + 15 = -14.662878299

Reorder the terms:
15 + x = -14.662878299

Solving
15 + x = -14.662878299

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -14.662878299 + -15

Combine like terms: 15 + -15 = 0
0 + x = -14.662878299 + -15
x = -14.662878299 + -15

Combine like terms: -14.662878299 + -15 = -29.662878299
x = -29.662878299

Simplifying
x = -29.662878299


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.337121701, -29.662878299}

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