x^2+3.5x-261=0

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Solution for x^2+3.5x-261=0 equation: 


Simplifying
x2 + 3.5x + -261 = 0

Reorder the terms:
-261 + 3.5x + x2 = 0

Solving
-261 + 3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '261' to each side of the equation.
-261 + 3.5x + 261 + x2 = 0 + 261

Reorder the terms:
-261 + 261 + 3.5x + x2 = 0 + 261

Combine like terms: -261 + 261 = 0
0 + 3.5x + x2 = 0 + 261
3.5x + x2 = 0 + 261

Combine like terms: 0 + 261 = 261
3.5x + x2 = 261

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 261 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 261 + 3.0625

Combine like terms: 261 + 3.0625 = 264.0625
3.0625 + 3.5x + x2 = 264.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 264.0625

Calculate the square root of the right side: 16.25

Break this problem into two subproblems by setting 
(x + 1.75) equal to 16.25 and -16.25.


Subproblem 1
x + 1.75 = 16.25

Simplifying
x + 1.75 = 16.25

Reorder the terms:
1.75 + x = 16.25

Solving
1.75 + x = 16.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 16.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 16.25 + -1.75
x = 16.25 + -1.75

Combine like terms: 16.25 + -1.75 = 14.5
x = 14.5

Simplifying
x = 14.5


Subproblem 2
x + 1.75 = -16.25

Simplifying
x + 1.75 = -16.25

Reorder the terms:
1.75 + x = -16.25

Solving
1.75 + x = -16.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -16.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -16.25 + -1.75
x = -16.25 + -1.75

Combine like terms: -16.25 + -1.75 = -18
x = -18

Simplifying
x = -18


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.5, -18}

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