x^2+148x+2501=0

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Solution for x^2+148x+2501=0 equation: 


Simplifying
x2 + 148x + 2501 = 0

Reorder the terms:
2501 + 148x + x2 = 0

Solving
2501 + 148x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2501' to each side of the equation.
2501 + 148x + -2501 + x2 = 0 + -2501

Reorder the terms:
2501 + -2501 + 148x + x2 = 0 + -2501

Combine like terms: 2501 + -2501 = 0
0 + 148x + x2 = 0 + -2501
148x + x2 = 0 + -2501

Combine like terms: 0 + -2501 = -2501
148x + x2 = -2501

The x term is 148x.  Take half its coefficient (74).
Square it (5476) and add it to both sides.

Add '5476' to each side of the equation.
148x + 5476 + x2 = -2501 + 5476

Reorder the terms:
5476 + 148x + x2 = -2501 + 5476

Combine like terms: -2501 + 5476 = 2975
5476 + 148x + x2 = 2975

Factor a perfect square on the left side:
(x + 74)(x + 74) = 2975

Calculate the square root of the right side: 54.543560573

Break this problem into two subproblems by setting 
(x + 74) equal to 54.543560573 and -54.543560573.


Subproblem 1
x + 74 = 54.543560573

Simplifying
x + 74 = 54.543560573

Reorder the terms:
74 + x = 54.543560573

Solving
74 + x = 54.543560573

Solving for variable 'x'.

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

Add '-74' to each side of the equation.
74 + -74 + x = 54.543560573 + -74

Combine like terms: 74 + -74 = 0
0 + x = 54.543560573 + -74
x = 54.543560573 + -74

Combine like terms: 54.543560573 + -74 = -19.456439427
x = -19.456439427

Simplifying
x = -19.456439427


Subproblem 2
x + 74 = -54.543560573

Simplifying
x + 74 = -54.543560573

Reorder the terms:
74 + x = -54.543560573

Solving
74 + x = -54.543560573

Solving for variable 'x'.

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

Add '-74' to each side of the equation.
74 + -74 + x = -54.543560573 + -74

Combine like terms: 74 + -74 = 0
0 + x = -54.543560573 + -74
x = -54.543560573 + -74

Combine like terms: -54.543560573 + -74 = -128.543560573
x = -128.543560573

Simplifying
x = -128.543560573


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-19.456439427, -128.543560573}

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