x^2+7.5x-4=0

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Solution for x^2+7.5x-4=0 equation: 


Simplifying
x2 + 7.5x + -4 = 0

Reorder the terms:
-4 + 7.5x + x2 = 0

Solving
-4 + 7.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 7.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 7.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 7.5x + x2 = 0 + 4
7.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
7.5x + x2 = 4

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 4 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 4 + 14.0625

Combine like terms: 4 + 14.0625 = 18.0625
14.0625 + 7.5x + x2 = 18.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 18.0625

Calculate the square root of the right side: 4.25

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.25 and -4.25.


Subproblem 1
x + 3.75 = 4.25

Simplifying
x + 3.75 = 4.25

Reorder the terms:
3.75 + x = 4.25

Solving
3.75 + x = 4.25

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 4.25 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 4.25 + -3.75
x = 4.25 + -3.75

Combine like terms: 4.25 + -3.75 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 3.75 = -4.25

Simplifying
x + 3.75 = -4.25

Reorder the terms:
3.75 + x = -4.25

Solving
3.75 + x = -4.25

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -4.25 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -4.25 + -3.75
x = -4.25 + -3.75

Combine like terms: -4.25 + -3.75 = -8
x = -8

Simplifying
x = -8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -8}

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