X^2+5X=93.75

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Solution for X^2+5X=93.75 equation: 


Simplifying
X2 + 5X = 93.75

Reorder the terms:
5X + X2 = 93.75

Solving
5X + X2 = 93.75

Solving for variable 'X'.

Reorder the terms:
-93.75 + 5X + X2 = 93.75 + -93.75

Combine like terms: 93.75 + -93.75 = 0.00
-93.75 + 5X + X2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '93.75' to each side of the equation.
-93.75 + 5X + 93.75 + X2 = 0.00 + 93.75

Reorder the terms:
-93.75 + 93.75 + 5X + X2 = 0.00 + 93.75

Combine like terms: -93.75 + 93.75 = 0.00
0.00 + 5X + X2 = 0.00 + 93.75
5X + X2 = 0.00 + 93.75

Combine like terms: 0.00 + 93.75 = 93.75
5X + X2 = 93.75

The X term is 5X.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5X + 6.25 + X2 = 93.75 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 93.75 + 6.25

Combine like terms: 93.75 + 6.25 = 100
6.25 + 5X + X2 = 100

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 100

Calculate the square root of the right side: 10

Break this problem into two subproblems by setting 
(X + 2.5) equal to 10 and -10.


Subproblem 1
X + 2.5 = 10

Simplifying
X + 2.5 = 10

Reorder the terms:
2.5 + X = 10

Solving
2.5 + X = 10

Solving for variable 'X'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + X = 10 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 10 + -2.5
X = 10 + -2.5

Combine like terms: 10 + -2.5 = 7.5
X = 7.5

Simplifying
X = 7.5


Subproblem 2
X + 2.5 = -10

Simplifying
X + 2.5 = -10

Reorder the terms:
2.5 + X = -10

Solving
2.5 + X = -10

Solving for variable 'X'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + X = -10 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -10 + -2.5
X = -10 + -2.5

Combine like terms: -10 + -2.5 = -12.5
X = -12.5

Simplifying
X = -12.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {7.5, -12.5}

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