x^2-35x-24=0

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Solution for x^2-35x-24=0 equation: 


Simplifying
x2 + -35x + -24 = 0

Reorder the terms:
-24 + -35x + x2 = 0

Solving
-24 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -35x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -35x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -35x + x2 = 0 + 24
-35x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-35x + x2 = 24

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 = 24 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 24 + 306.25

Combine like terms: 24 + 306.25 = 330.25
306.25 + -35x + x2 = 330.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 330.25

Calculate the square root of the right side: 18.172781845

Break this problem into two subproblems by setting 
(x + -17.5) equal to 18.172781845 and -18.172781845.


Subproblem 1
x + -17.5 = 18.172781845

Simplifying
x + -17.5 = 18.172781845

Reorder the terms:
-17.5 + x = 18.172781845

Solving
-17.5 + x = 18.172781845

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 = 18.172781845 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 18.172781845 + 17.5
x = 18.172781845 + 17.5

Combine like terms: 18.172781845 + 17.5 = 35.672781845
x = 35.672781845

Simplifying
x = 35.672781845


Subproblem 2
x + -17.5 = -18.172781845

Simplifying
x + -17.5 = -18.172781845

Reorder the terms:
-17.5 + x = -18.172781845

Solving
-17.5 + x = -18.172781845

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 = -18.172781845 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -18.172781845 + 17.5
x = -18.172781845 + 17.5

Combine like terms: -18.172781845 + 17.5 = -0.672781845
x = -0.672781845

Simplifying
x = -0.672781845


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.672781845, -0.672781845}

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