x^2-35x+262=0

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Solution for x^2-35x+262=0 equation: 


Simplifying
x2 + -35x + 262 = 0

Reorder the terms:
262 + -35x + x2 = 0

Solving
262 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-262' to each side of the equation.
262 + -35x + -262 + x2 = 0 + -262

Reorder the terms:
262 + -262 + -35x + x2 = 0 + -262

Combine like terms: 262 + -262 = 0
0 + -35x + x2 = 0 + -262
-35x + x2 = 0 + -262

Combine like terms: 0 + -262 = -262
-35x + x2 = -262

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -262 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -262 + 306.25

Combine like terms: -262 + 306.25 = 44.25
306.25 + -35x + x2 = 44.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + -17.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
x + -17.5 = 6.652067348

Simplifying
x + -17.5 = 6.652067348

Reorder the terms:
-17.5 + x = 6.652067348

Solving
-17.5 + x = 6.652067348

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 6.652067348 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 6.652067348 + 17.5
x = 6.652067348 + 17.5

Combine like terms: 6.652067348 + 17.5 = 24.152067348
x = 24.152067348

Simplifying
x = 24.152067348


Subproblem 2
x + -17.5 = -6.652067348

Simplifying
x + -17.5 = -6.652067348

Reorder the terms:
-17.5 + x = -6.652067348

Solving
-17.5 + x = -6.652067348

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -6.652067348 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -6.652067348 + 17.5
x = -6.652067348 + 17.5

Combine like terms: -6.652067348 + 17.5 = 10.847932652
x = 10.847932652

Simplifying
x = 10.847932652


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.152067348, 10.847932652}

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