5x^2-7x-70=0

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Solution for 5x^2-7x-70=0 equation: 


Simplifying
5x2 + -7x + -70 = 0

Reorder the terms:
-70 + -7x + 5x2 = 0

Solving
-70 + -7x + 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 + -1.4x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -1.4x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -1.4x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1.4x + x2 = 0 + 14
-1.4x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-1.4x + x2 = 14

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 14 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 14 + 0.49

Combine like terms: 14 + 0.49 = 14.49
0.49 + -1.4x + x2 = 14.49

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 14.49

Calculate the square root of the right side: 3.806573262

Break this problem into two subproblems by setting 
(x + -0.7) equal to 3.806573262 and -3.806573262.


Subproblem 1
x + -0.7 = 3.806573262

Simplifying
x + -0.7 = 3.806573262

Reorder the terms:
-0.7 + x = 3.806573262

Solving
-0.7 + x = 3.806573262

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 3.806573262 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 3.806573262 + 0.7
x = 3.806573262 + 0.7

Combine like terms: 3.806573262 + 0.7 = 4.506573262
x = 4.506573262

Simplifying
x = 4.506573262


Subproblem 2
x + -0.7 = -3.806573262

Simplifying
x + -0.7 = -3.806573262

Reorder the terms:
-0.7 + x = -3.806573262

Solving
-0.7 + x = -3.806573262

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -3.806573262 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -3.806573262 + 0.7
x = -3.806573262 + 0.7

Combine like terms: -3.806573262 + 0.7 = -3.106573262
x = -3.106573262

Simplifying
x = -3.106573262


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.506573262, -3.106573262}

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