4.9x^2-25x-70=0

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Solution for 4.9x^2-25x-70=0 equation: 


Simplifying
4.9x2 + -25x + -70 = 0

Reorder the terms:
-70 + -25x + 4.9x2 = 0

Solving
-70 + -25x + 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 + -5.102040816x + x2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + -5.102040816x + 14.28571429 + x2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + -5.102040816x + x2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + -5.102040816x + x2 = 0 + 14.28571429
-5.102040816x + x2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
-5.102040816x + x2 = 14.28571429

The x term is -5.102040816x.  Take half its coefficient (-2.551020408).
Square it (6.507705122) and add it to both sides.

Add '6.507705122' to each side of the equation.
-5.102040816x + 6.507705122 + x2 = 14.28571429 + 6.507705122

Reorder the terms:
6.507705122 + -5.102040816x + x2 = 14.28571429 + 6.507705122

Combine like terms: 14.28571429 + 6.507705122 = 20.793419412
6.507705122 + -5.102040816x + x2 = 20.793419412

Factor a perfect square on the left side:
(x + -2.551020408)(x + -2.551020408) = 20.793419412

Calculate the square root of the right side: 4.559980199

Break this problem into two subproblems by setting 
(x + -2.551020408) equal to 4.559980199 and -4.559980199.


Subproblem 1
x + -2.551020408 = 4.559980199

Simplifying
x + -2.551020408 = 4.559980199

Reorder the terms:
-2.551020408 + x = 4.559980199

Solving
-2.551020408 + x = 4.559980199

Solving for variable 'x'.

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

Add '2.551020408' to each side of the equation.
-2.551020408 + 2.551020408 + x = 4.559980199 + 2.551020408

Combine like terms: -2.551020408 + 2.551020408 = 0.000000000
0.000000000 + x = 4.559980199 + 2.551020408
x = 4.559980199 + 2.551020408

Combine like terms: 4.559980199 + 2.551020408 = 7.111000607
x = 7.111000607

Simplifying
x = 7.111000607


Subproblem 2
x + -2.551020408 = -4.559980199

Simplifying
x + -2.551020408 = -4.559980199

Reorder the terms:
-2.551020408 + x = -4.559980199

Solving
-2.551020408 + x = -4.559980199

Solving for variable 'x'.

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

Add '2.551020408' to each side of the equation.
-2.551020408 + 2.551020408 + x = -4.559980199 + 2.551020408

Combine like terms: -2.551020408 + 2.551020408 = 0.000000000
0.000000000 + x = -4.559980199 + 2.551020408
x = -4.559980199 + 2.551020408

Combine like terms: -4.559980199 + 2.551020408 = -2.008959791
x = -2.008959791

Simplifying
x = -2.008959791


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.111000607, -2.008959791}

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