x^2-15x-148=0

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Solution for x^2-15x-148=0 equation: 


Simplifying
x2 + -15x + -148 = 0

Reorder the terms:
-148 + -15x + x2 = 0

Solving
-148 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '148' to each side of the equation.
-148 + -15x + 148 + x2 = 0 + 148

Reorder the terms:
-148 + 148 + -15x + x2 = 0 + 148

Combine like terms: -148 + 148 = 0
0 + -15x + x2 = 0 + 148
-15x + x2 = 0 + 148

Combine like terms: 0 + 148 = 148
-15x + x2 = 148

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 148 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 148 + 56.25

Combine like terms: 148 + 56.25 = 204.25
56.25 + -15x + x2 = 204.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 204.25

Calculate the square root of the right side: 14.291605928

Break this problem into two subproblems by setting 
(x + -7.5) equal to 14.291605928 and -14.291605928.


Subproblem 1
x + -7.5 = 14.291605928

Simplifying
x + -7.5 = 14.291605928

Reorder the terms:
-7.5 + x = 14.291605928

Solving
-7.5 + x = 14.291605928

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 14.291605928 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 14.291605928 + 7.5
x = 14.291605928 + 7.5

Combine like terms: 14.291605928 + 7.5 = 21.791605928
x = 21.791605928

Simplifying
x = 21.791605928


Subproblem 2
x + -7.5 = -14.291605928

Simplifying
x + -7.5 = -14.291605928

Reorder the terms:
-7.5 + x = -14.291605928

Solving
-7.5 + x = -14.291605928

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -14.291605928 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -14.291605928 + 7.5
x = -14.291605928 + 7.5

Combine like terms: -14.291605928 + 7.5 = -6.791605928
x = -6.791605928

Simplifying
x = -6.791605928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.791605928, -6.791605928}

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