x^2+7x-259=0

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Solution for x^2+7x-259=0 equation: 


Simplifying
x2 + 7x + -259 = 0

Reorder the terms:
-259 + 7x + x2 = 0

Solving
-259 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '259' to each side of the equation.
-259 + 7x + 259 + x2 = 0 + 259

Reorder the terms:
-259 + 259 + 7x + x2 = 0 + 259

Combine like terms: -259 + 259 = 0
0 + 7x + x2 = 0 + 259
7x + x2 = 0 + 259

Combine like terms: 0 + 259 = 259
7x + x2 = 259

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 259 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 259 + 12.25

Combine like terms: 259 + 12.25 = 271.25
12.25 + 7x + x2 = 271.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 271.25

Calculate the square root of the right side: 16.469669092

Break this problem into two subproblems by setting 
(x + 3.5) equal to 16.469669092 and -16.469669092.


Subproblem 1
x + 3.5 = 16.469669092

Simplifying
x + 3.5 = 16.469669092

Reorder the terms:
3.5 + x = 16.469669092

Solving
3.5 + x = 16.469669092

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 16.469669092 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 16.469669092 + -3.5
x = 16.469669092 + -3.5

Combine like terms: 16.469669092 + -3.5 = 12.969669092
x = 12.969669092

Simplifying
x = 12.969669092


Subproblem 2
x + 3.5 = -16.469669092

Simplifying
x + 3.5 = -16.469669092

Reorder the terms:
3.5 + x = -16.469669092

Solving
3.5 + x = -16.469669092

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -16.469669092 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -16.469669092 + -3.5
x = -16.469669092 + -3.5

Combine like terms: -16.469669092 + -3.5 = -19.969669092
x = -19.969669092

Simplifying
x = -19.969669092


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.969669092, -19.969669092}

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