4.9x^2-12x-70=0

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Solution for 4.9x^2-12x-70=0 equation: 


Simplifying
4.9x2 + -12x + -70 = 0

Reorder the terms:
-70 + -12x + 4.9x2 = 0

Solving
-70 + -12x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
-14.28571429 + -2.448979592x + x2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + -2.448979592x + 14.28571429 + x2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + -2.448979592x + x2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + -2.448979592x + x2 = 0 + 14.28571429
-2.448979592x + x2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
-2.448979592x + x2 = 14.28571429

The x term is -2.448979592x.  Take half its coefficient (-1.224489796).
Square it (1.499375261) and add it to both sides.

Add '1.499375261' to each side of the equation.
-2.448979592x + 1.499375261 + x2 = 14.28571429 + 1.499375261

Reorder the terms:
1.499375261 + -2.448979592x + x2 = 14.28571429 + 1.499375261

Combine like terms: 14.28571429 + 1.499375261 = 15.785089551
1.499375261 + -2.448979592x + x2 = 15.785089551

Factor a perfect square on the left side:
(x + -1.224489796)(x + -1.224489796) = 15.785089551

Calculate the square root of the right side: 3.973045375

Break this problem into two subproblems by setting 
(x + -1.224489796) equal to 3.973045375 and -3.973045375.


Subproblem 1
x + -1.224489796 = 3.973045375

Simplifying
x + -1.224489796 = 3.973045375

Reorder the terms:
-1.224489796 + x = 3.973045375

Solving
-1.224489796 + x = 3.973045375

Solving for variable 'x'.

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

Add '1.224489796' to each side of the equation.
-1.224489796 + 1.224489796 + x = 3.973045375 + 1.224489796

Combine like terms: -1.224489796 + 1.224489796 = 0.000000000
0.000000000 + x = 3.973045375 + 1.224489796
x = 3.973045375 + 1.224489796

Combine like terms: 3.973045375 + 1.224489796 = 5.197535171
x = 5.197535171

Simplifying
x = 5.197535171


Subproblem 2
x + -1.224489796 = -3.973045375

Simplifying
x + -1.224489796 = -3.973045375

Reorder the terms:
-1.224489796 + x = -3.973045375

Solving
-1.224489796 + x = -3.973045375

Solving for variable 'x'.

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

Add '1.224489796' to each side of the equation.
-1.224489796 + 1.224489796 + x = -3.973045375 + 1.224489796

Combine like terms: -1.224489796 + 1.224489796 = 0.000000000
0.000000000 + x = -3.973045375 + 1.224489796
x = -3.973045375 + 1.224489796

Combine like terms: -3.973045375 + 1.224489796 = -2.748555579
x = -2.748555579

Simplifying
x = -2.748555579


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.197535171, -2.748555579}

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