x^2-7.25x-57=0

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Solution for x^2-7.25x-57=0 equation: 


Simplifying
x2 + -7.25x + -57 = 0

Reorder the terms:
-57 + -7.25x + x2 = 0

Solving
-57 + -7.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + -7.25x + 57 + x2 = 0 + 57

Reorder the terms:
-57 + 57 + -7.25x + x2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + -7.25x + x2 = 0 + 57
-7.25x + x2 = 0 + 57

Combine like terms: 0 + 57 = 57
-7.25x + x2 = 57

The x term is -7.25x.  Take half its coefficient (-3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
-7.25x + 13.140625 + x2 = 57 + 13.140625

Reorder the terms:
13.140625 + -7.25x + x2 = 57 + 13.140625

Combine like terms: 57 + 13.140625 = 70.140625
13.140625 + -7.25x + x2 = 70.140625

Factor a perfect square on the left side:
(x + -3.625)(x + -3.625) = 70.140625

Calculate the square root of the right side: 8.375

Break this problem into two subproblems by setting 
(x + -3.625) equal to 8.375 and -8.375.


Subproblem 1
x + -3.625 = 8.375

Simplifying
x + -3.625 = 8.375

Reorder the terms:
-3.625 + x = 8.375

Solving
-3.625 + x = 8.375

Solving for variable 'x'.

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

Add '3.625' to each side of the equation.
-3.625 + 3.625 + x = 8.375 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + x = 8.375 + 3.625
x = 8.375 + 3.625

Combine like terms: 8.375 + 3.625 = 12
x = 12

Simplifying
x = 12


Subproblem 2
x + -3.625 = -8.375

Simplifying
x + -3.625 = -8.375

Reorder the terms:
-3.625 + x = -8.375

Solving
-3.625 + x = -8.375

Solving for variable 'x'.

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

Add '3.625' to each side of the equation.
-3.625 + 3.625 + x = -8.375 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + x = -8.375 + 3.625
x = -8.375 + 3.625

Combine like terms: -8.375 + 3.625 = -4.75
x = -4.75

Simplifying
x = -4.75


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12, -4.75}

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