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 = 282.25
306.25 + 35x + x2 = 282.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(x + 17.5) equal to 16.800297616 and -16.800297616.


Subproblem 1
x + 17.5 = 16.800297616

Simplifying
x + 17.5 = 16.800297616

Reorder the terms:
17.5 + x = 16.800297616

Solving
17.5 + x = 16.800297616

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 = 16.800297616 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 16.800297616 + -17.5
x = 16.800297616 + -17.5

Combine like terms: 16.800297616 + -17.5 = -0.699702384
x = -0.699702384

Simplifying
x = -0.699702384


Subproblem 2
x + 17.5 = -16.800297616

Simplifying
x + 17.5 = -16.800297616

Reorder the terms:
17.5 + x = -16.800297616

Solving
17.5 + x = -16.800297616

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 = -16.800297616 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -16.800297616 + -17.5
x = -16.800297616 + -17.5

Combine like terms: -16.800297616 + -17.5 = -34.300297616
x = -34.300297616

Simplifying
x = -34.300297616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.699702384, -34.300297616}

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