5x^2+70x+75=0

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Solution for 5x^2+70x+75=0 equation: 


Simplifying
5x2 + 70x + 75 = 0

Reorder the terms:
75 + 70x + 5x2 = 0

Solving
75 + 70x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + 14x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(15 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
15 + 14x + x2 = 0

Solving
15 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 14x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 14x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 14x + x2 = 0 + -15
14x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
14x + x2 = -15

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -15 + 49

Reorder the terms:
49 + 14x + x2 = -15 + 49

Combine like terms: -15 + 49 = 34
49 + 14x + x2 = 34

Factor a perfect square on the left side:
(x + 7)(x + 7) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + 7) equal to 5.830951895 and -5.830951895.


Subproblem 1
x + 7 = 5.830951895

Simplifying
x + 7 = 5.830951895

Reorder the terms:
7 + x = 5.830951895

Solving
7 + x = 5.830951895

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 5.830951895 + -7

Combine like terms: 7 + -7 = 0
0 + x = 5.830951895 + -7
x = 5.830951895 + -7

Combine like terms: 5.830951895 + -7 = -1.169048105
x = -1.169048105

Simplifying
x = -1.169048105


Subproblem 2
x + 7 = -5.830951895

Simplifying
x + 7 = -5.830951895

Reorder the terms:
7 + x = -5.830951895

Solving
7 + x = -5.830951895

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -5.830951895 + -7

Combine like terms: 7 + -7 = 0
0 + x = -5.830951895 + -7
x = -5.830951895 + -7

Combine like terms: -5.830951895 + -7 = -12.830951895
x = -12.830951895

Simplifying
x = -12.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.169048105, -12.830951895}
Solution
x = {-1.169048105, -12.830951895}

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