7x^2+14x-25=0

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Solution for 7x^2+14x-25=0 equation: 


Simplifying
7x2 + 14x + -25 = 0

Reorder the terms:
-25 + 14x + 7x2 = 0

Solving
-25 + 14x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-3.571428571 + 2x + x2 = 0

Move the constant term to the right:

Add '3.571428571' to each side of the equation.
-3.571428571 + 2x + 3.571428571 + x2 = 0 + 3.571428571

Reorder the terms:
-3.571428571 + 3.571428571 + 2x + x2 = 0 + 3.571428571

Combine like terms: -3.571428571 + 3.571428571 = 0.000000000
0.000000000 + 2x + x2 = 0 + 3.571428571
2x + x2 = 0 + 3.571428571

Combine like terms: 0 + 3.571428571 = 3.571428571
2x + x2 = 3.571428571

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 3.571428571 + 1

Reorder the terms:
1 + 2x + x2 = 3.571428571 + 1

Combine like terms: 3.571428571 + 1 = 4.571428571
1 + 2x + x2 = 4.571428571

Factor a perfect square on the left side:
(x + 1)(x + 1) = 4.571428571

Calculate the square root of the right side: 2.138089935

Break this problem into two subproblems by setting 
(x + 1) equal to 2.138089935 and -2.138089935.


Subproblem 1
x + 1 = 2.138089935

Simplifying
x + 1 = 2.138089935

Reorder the terms:
1 + x = 2.138089935

Solving
1 + x = 2.138089935

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.138089935 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.138089935 + -1
x = 2.138089935 + -1

Combine like terms: 2.138089935 + -1 = 1.138089935
x = 1.138089935

Simplifying
x = 1.138089935


Subproblem 2
x + 1 = -2.138089935

Simplifying
x + 1 = -2.138089935

Reorder the terms:
1 + x = -2.138089935

Solving
1 + x = -2.138089935

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.138089935 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.138089935 + -1
x = -2.138089935 + -1

Combine like terms: -2.138089935 + -1 = -3.138089935
x = -3.138089935

Simplifying
x = -3.138089935


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.138089935, -3.138089935}

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