-5x^2-18x+70=0

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Solution for -5x^2-18x+70=0 equation:


Simplifying
-5x2 + -18x + 70 = 0

Reorder the terms:
70 + -18x + -5x2 = 0

Solving
70 + -18x + -5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-14 + 3.6x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 3.6x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 3.6x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3.6x + x2 = 0 + 14
3.6x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
3.6x + x2 = 14

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = 14 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = 14 + 3.24

Combine like terms: 14 + 3.24 = 17.24
3.24 + 3.6x + x2 = 17.24

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 17.24

Calculate the square root of the right side: 4.152107898

Break this problem into two subproblems by setting 
(x + 1.8) equal to 4.152107898 and -4.152107898.


Subproblem 1
x + 1.8 = 4.152107898

Simplifying
x + 1.8 = 4.152107898

Reorder the terms:
1.8 + x = 4.152107898

Solving
1.8 + x = 4.152107898

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = 4.152107898 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = 4.152107898 + -1.8
x = 4.152107898 + -1.8

Combine like terms: 4.152107898 + -1.8 = 2.352107898
x = 2.352107898

Simplifying
x = 2.352107898


Subproblem 2
x + 1.8 = -4.152107898

Simplifying
x + 1.8 = -4.152107898

Reorder the terms:
1.8 + x = -4.152107898

Solving
1.8 + x = -4.152107898

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = -4.152107898 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = -4.152107898 + -1.8
x = -4.152107898 + -1.8

Combine like terms: -4.152107898 + -1.8 = -5.952107898
x = -5.952107898

Simplifying
x = -5.952107898


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.352107898, -5.952107898}

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