2.5x^2-14x-49=0

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Solution for 2.5x^2-14x-49=0 equation: 


Simplifying
2.5x2 + -14x + -49 = 0

Reorder the terms:
-49 + -14x + 2.5x2 = 0

Solving
-49 + -14x + 2.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.5'.
-19.6 + -5.6x + x2 = 0

Move the constant term to the right:

Add '19.6' to each side of the equation.
-19.6 + -5.6x + 19.6 + x2 = 0 + 19.6

Reorder the terms:
-19.6 + 19.6 + -5.6x + x2 = 0 + 19.6

Combine like terms: -19.6 + 19.6 = 0.0
0.0 + -5.6x + x2 = 0 + 19.6
-5.6x + x2 = 0 + 19.6

Combine like terms: 0 + 19.6 = 19.6
-5.6x + x2 = 19.6

The x term is -5.6x.  Take half its coefficient (-2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
-5.6x + 7.84 + x2 = 19.6 + 7.84

Reorder the terms:
7.84 + -5.6x + x2 = 19.6 + 7.84

Combine like terms: 19.6 + 7.84 = 27.44
7.84 + -5.6x + x2 = 27.44

Factor a perfect square on the left side:
(x + -2.8)(x + -2.8) = 27.44

Calculate the square root of the right side: 5.238320341

Break this problem into two subproblems by setting 
(x + -2.8) equal to 5.238320341 and -5.238320341.


Subproblem 1
x + -2.8 = 5.238320341

Simplifying
x + -2.8 = 5.238320341

Reorder the terms:
-2.8 + x = 5.238320341

Solving
-2.8 + x = 5.238320341

Solving for variable 'x'.

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

Add '2.8' to each side of the equation.
-2.8 + 2.8 + x = 5.238320341 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + x = 5.238320341 + 2.8
x = 5.238320341 + 2.8

Combine like terms: 5.238320341 + 2.8 = 8.038320341
x = 8.038320341

Simplifying
x = 8.038320341


Subproblem 2
x + -2.8 = -5.238320341

Simplifying
x + -2.8 = -5.238320341

Reorder the terms:
-2.8 + x = -5.238320341

Solving
-2.8 + x = -5.238320341

Solving for variable 'x'.

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

Add '2.8' to each side of the equation.
-2.8 + 2.8 + x = -5.238320341 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + x = -5.238320341 + 2.8
x = -5.238320341 + 2.8

Combine like terms: -5.238320341 + 2.8 = -2.438320341
x = -2.438320341

Simplifying
x = -2.438320341


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.038320341, -2.438320341}

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