7x^2-105x-49=0

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Solution for 7x^2-105x-49=0 equation: 


Simplifying
7x2 + -105x + -49 = 0

Reorder the terms:
-49 + -105x + 7x2 = 0

Solving
-49 + -105x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + -15x + x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-7 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + -15x + x2 = 0

Solving
-7 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -15x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -15x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -15x + x2 = 0 + 7
-15x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-15x + x2 = 7

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 7 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 7 + 56.25

Combine like terms: 7 + 56.25 = 63.25
56.25 + -15x + x2 = 63.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 63.25

Calculate the square root of the right side: 7.95298686

Break this problem into two subproblems by setting 
(x + -7.5) equal to 7.95298686 and -7.95298686.


Subproblem 1
x + -7.5 = 7.95298686

Simplifying
x + -7.5 = 7.95298686

Reorder the terms:
-7.5 + x = 7.95298686

Solving
-7.5 + x = 7.95298686

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 7.95298686 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 7.95298686 + 7.5
x = 7.95298686 + 7.5

Combine like terms: 7.95298686 + 7.5 = 15.45298686
x = 15.45298686

Simplifying
x = 15.45298686


Subproblem 2
x + -7.5 = -7.95298686

Simplifying
x + -7.5 = -7.95298686

Reorder the terms:
-7.5 + x = -7.95298686

Solving
-7.5 + x = -7.95298686

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -7.95298686 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -7.95298686 + 7.5
x = -7.95298686 + 7.5

Combine like terms: -7.95298686 + 7.5 = -0.45298686
x = -0.45298686

Simplifying
x = -0.45298686


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.45298686, -0.45298686}
Solution
x = {15.45298686, -0.45298686}

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