4x^2-7x-70=0

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Solution for 4x^2-7x-70=0 equation: 


Simplifying
4x2 + -7x + -70 = 0

Reorder the terms:
-70 + -7x + 4x2 = 0

Solving
-70 + -7x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-17.5 + -1.75x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -1.75x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -1.75x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -1.75x + x2 = 0 + 17.5
-1.75x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-1.75x + x2 = 17.5

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 17.5 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 17.5 + 0.765625

Combine like terms: 17.5 + 0.765625 = 18.265625
0.765625 + -1.75x + x2 = 18.265625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 18.265625

Calculate the square root of the right side: 4.273830249

Break this problem into two subproblems by setting 
(x + -0.875) equal to 4.273830249 and -4.273830249.


Subproblem 1
x + -0.875 = 4.273830249

Simplifying
x + -0.875 = 4.273830249

Reorder the terms:
-0.875 + x = 4.273830249

Solving
-0.875 + x = 4.273830249

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 4.273830249 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 4.273830249 + 0.875
x = 4.273830249 + 0.875

Combine like terms: 4.273830249 + 0.875 = 5.148830249
x = 5.148830249

Simplifying
x = 5.148830249


Subproblem 2
x + -0.875 = -4.273830249

Simplifying
x + -0.875 = -4.273830249

Reorder the terms:
-0.875 + x = -4.273830249

Solving
-0.875 + x = -4.273830249

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -4.273830249 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -4.273830249 + 0.875
x = -4.273830249 + 0.875

Combine like terms: -4.273830249 + 0.875 = -3.398830249
x = -3.398830249

Simplifying
x = -3.398830249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.148830249, -3.398830249}

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