x^2+48x-1400=0

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Solution for x^2+48x-1400=0 equation: 


Simplifying
x2 + 48x + -1400 = 0

Reorder the terms:
-1400 + 48x + x2 = 0

Solving
-1400 + 48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1400' to each side of the equation.
-1400 + 48x + 1400 + x2 = 0 + 1400

Reorder the terms:
-1400 + 1400 + 48x + x2 = 0 + 1400

Combine like terms: -1400 + 1400 = 0
0 + 48x + x2 = 0 + 1400
48x + x2 = 0 + 1400

Combine like terms: 0 + 1400 = 1400
48x + x2 = 1400

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = 1400 + 576

Reorder the terms:
576 + 48x + x2 = 1400 + 576

Combine like terms: 1400 + 576 = 1976
576 + 48x + x2 = 1976

Factor a perfect square on the left side:
(x + 24)(x + 24) = 1976

Calculate the square root of the right side: 44.452221542

Break this problem into two subproblems by setting 
(x + 24) equal to 44.452221542 and -44.452221542.


Subproblem 1
x + 24 = 44.452221542

Simplifying
x + 24 = 44.452221542

Reorder the terms:
24 + x = 44.452221542

Solving
24 + x = 44.452221542

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = 44.452221542 + -24

Combine like terms: 24 + -24 = 0
0 + x = 44.452221542 + -24
x = 44.452221542 + -24

Combine like terms: 44.452221542 + -24 = 20.452221542
x = 20.452221542

Simplifying
x = 20.452221542


Subproblem 2
x + 24 = -44.452221542

Simplifying
x + 24 = -44.452221542

Reorder the terms:
24 + x = -44.452221542

Solving
24 + x = -44.452221542

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = -44.452221542 + -24

Combine like terms: 24 + -24 = 0
0 + x = -44.452221542 + -24
x = -44.452221542 + -24

Combine like terms: -44.452221542 + -24 = -68.452221542
x = -68.452221542

Simplifying
x = -68.452221542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.452221542, -68.452221542}

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