=x^2+24x+145

Solution for =x^2+24x+145 equation:

Simplifying
0 = x2 + 24x + 145

Reorder the terms:
0 = 145 + 24x + x2

Solving
0 = 145 + 24x + x2

Solving for variable 'x'.

Combine like terms: 0 + -145 = -145
-145 + -24x + -1x2 = 145 + 24x + x2 + -145 + -24x + -1x2

Reorder the terms:
-145 + -24x + -1x2 = 145 + -145 + 24x + -24x + x2 + -1x2

Combine like terms: 145 + -145 = 0
-145 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2
-145 + -24x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
-145 + -24x + -1x2 = 0 + x2 + -1x2
-145 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-145 + -24x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(145 + 24x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(145 + 24x + x2)' equal to zero and attempt to solve:

Simplifying
145 + 24x + x2 = 0

Solving
145 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-145' to each side of the equation.
145 + 24x + -145 + x2 = 0 + -145

Reorder the terms:
145 + -145 + 24x + x2 = 0 + -145

Combine like terms: 145 + -145 = 0
0 + 24x + x2 = 0 + -145
24x + x2 = 0 + -145

Combine like terms: 0 + -145 = -145
24x + x2 = -145

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = -145 + 144

Reorder the terms:
144 + 24x + x2 = -145 + 144

Combine like terms: -145 + 144 = -1
144 + 24x + x2 = -1

Factor a perfect square on the left side:
(x + 12)(x + 12) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.