x^2+47x-24=0

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Solution for x^2+47x-24=0 equation: 


Simplifying
x2 + 47x + -24 = 0

Reorder the terms:
-24 + 47x + x2 = 0

Solving
-24 + 47x + 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 + 47x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 47x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 47x + x2 = 0 + 24
47x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
47x + x2 = 24

The x term is 47x.  Take half its coefficient (23.5).
Square it (552.25) and add it to both sides.

Add '552.25' to each side of the equation.
47x + 552.25 + x2 = 24 + 552.25

Reorder the terms:
552.25 + 47x + x2 = 24 + 552.25

Combine like terms: 24 + 552.25 = 576.25
552.25 + 47x + x2 = 576.25

Factor a perfect square on the left side:
(x + 23.5)(x + 23.5) = 576.25

Calculate the square root of the right side: 24.005207768

Break this problem into two subproblems by setting 
(x + 23.5) equal to 24.005207768 and -24.005207768.


Subproblem 1
x + 23.5 = 24.005207768

Simplifying
x + 23.5 = 24.005207768

Reorder the terms:
23.5 + x = 24.005207768

Solving
23.5 + x = 24.005207768

Solving for variable 'x'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + x = 24.005207768 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = 24.005207768 + -23.5
x = 24.005207768 + -23.5

Combine like terms: 24.005207768 + -23.5 = 0.505207768
x = 0.505207768

Simplifying
x = 0.505207768


Subproblem 2
x + 23.5 = -24.005207768

Simplifying
x + 23.5 = -24.005207768

Reorder the terms:
23.5 + x = -24.005207768

Solving
23.5 + x = -24.005207768

Solving for variable 'x'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + x = -24.005207768 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = -24.005207768 + -23.5
x = -24.005207768 + -23.5

Combine like terms: -24.005207768 + -23.5 = -47.505207768
x = -47.505207768

Simplifying
x = -47.505207768


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.505207768, -47.505207768}

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