(x+24)(x+23)=1174.25

Solution for (x+24)(x+23)=1174.25 equation:

Simplifying
(x + 24)(x + 23) = 1174.25

Reorder the terms:
(24 + x)(x + 23) = 1174.25

Reorder the terms:
(24 + x)(23 + x) = 1174.25

Multiply (24 + x) * (23 + x)
(24(23 + x) + x(23 + x)) = 1174.25
((23 * 24 + x * 24) + x(23 + x)) = 1174.25
((552 + 24x) + x(23 + x)) = 1174.25
(552 + 24x + (23 * x + x * x)) = 1174.25
(552 + 24x + (23x + x2)) = 1174.25

Combine like terms: 24x + 23x = 47x
(552 + 47x + x2) = 1174.25

Solving
552 + 47x + x2 = 1174.25

Solving for variable 'x'.

Reorder the terms:
552 + -1174.25 + 47x + x2 = 1174.25 + -1174.25

Combine like terms: 552 + -1174.25 = -622.25
-622.25 + 47x + x2 = 1174.25 + -1174.25

Combine like terms: 1174.25 + -1174.25 = 0.00
-622.25 + 47x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '622.25' to each side of the equation.
-622.25 + 47x + 622.25 + x2 = 0.00 + 622.25

Reorder the terms:
-622.25 + 622.25 + 47x + x2 = 0.00 + 622.25

Combine like terms: -622.25 + 622.25 = 0.00
0.00 + 47x + x2 = 0.00 + 622.25
47x + x2 = 0.00 + 622.25

Combine like terms: 0.00 + 622.25 = 622.25
47x + x2 = 622.25

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 = 622.25 + 552.25

Reorder the terms:
552.25 + 47x + x2 = 622.25 + 552.25

Combine like terms: 622.25 + 552.25 = 1174.5
552.25 + 47x + x2 = 1174.5

Factor a perfect square on the left side:
(x + 23.5)(x + 23.5) = 1174.5

Calculate the square root of the right side: 34.270978976

Break this problem into two subproblems by setting 
(x + 23.5) equal to 34.270978976 and -34.270978976.

Subproblem 1
x + 23.5 = 34.270978976

Simplifying
x + 23.5 = 34.270978976

Reorder the terms:
23.5 + x = 34.270978976

Solving
23.5 + x = 34.270978976

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 = 34.270978976 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = 34.270978976 + -23.5
x = 34.270978976 + -23.5

Combine like terms: 34.270978976 + -23.5 = 10.770978976
x = 10.770978976

Simplifying
x = 10.770978976

Subproblem 2
x + 23.5 = -34.270978976

Simplifying
x + 23.5 = -34.270978976

Reorder the terms:
23.5 + x = -34.270978976

Solving
23.5 + x = -34.270978976

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 = -34.270978976 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = -34.270978976 + -23.5
x = -34.270978976 + -23.5

Combine like terms: -34.270978976 + -23.5 = -57.770978976
x = -57.770978976

Simplifying
x = -57.770978976

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.770978976, -57.770978976}