(x-15)(x+0.25)=0

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Solution for (x-15)(x+0.25)=0 equation: 


Simplifying
(x + -15)(x + 0.25) = 0

Reorder the terms:
(-15 + x)(x + 0.25) = 0

Reorder the terms:
(-15 + x)(0.25 + x) = 0

Multiply (-15 + x) * (0.25 + x)
(-15(0.25 + x) + x(0.25 + x)) = 0
((0.25 * -15 + x * -15) + x(0.25 + x)) = 0
((-3.75 + -15x) + x(0.25 + x)) = 0
(-3.75 + -15x + (0.25 * x + x * x)) = 0
(-3.75 + -15x + (0.25x + x2)) = 0

Combine like terms: -15x + 0.25x = -14.75x
(-3.75 + -14.75x + x2) = 0

Solving
-3.75 + -14.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -14.75x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -14.75x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -14.75x + x2 = 0 + 3.75
-14.75x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-14.75x + x2 = 3.75

The x term is -14.75x.  Take half its coefficient (-7.375).
Square it (54.390625) and add it to both sides.

Add '54.390625' to each side of the equation.
-14.75x + 54.390625 + x2 = 3.75 + 54.390625

Reorder the terms:
54.390625 + -14.75x + x2 = 3.75 + 54.390625

Combine like terms: 3.75 + 54.390625 = 58.140625
54.390625 + -14.75x + x2 = 58.140625

Factor a perfect square on the left side:
(x + -7.375)(x + -7.375) = 58.140625

Calculate the square root of the right side: 7.625

Break this problem into two subproblems by setting 
(x + -7.375) equal to 7.625 and -7.625.


Subproblem 1
x + -7.375 = 7.625

Simplifying
x + -7.375 = 7.625

Reorder the terms:
-7.375 + x = 7.625

Solving
-7.375 + x = 7.625

Solving for variable 'x'.

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

Add '7.375' to each side of the equation.
-7.375 + 7.375 + x = 7.625 + 7.375

Combine like terms: -7.375 + 7.375 = 0.000
0.000 + x = 7.625 + 7.375
x = 7.625 + 7.375

Combine like terms: 7.625 + 7.375 = 15
x = 15

Simplifying
x = 15


Subproblem 2
x + -7.375 = -7.625

Simplifying
x + -7.375 = -7.625

Reorder the terms:
-7.375 + x = -7.625

Solving
-7.375 + x = -7.625

Solving for variable 'x'.

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

Add '7.375' to each side of the equation.
-7.375 + 7.375 + x = -7.625 + 7.375

Combine like terms: -7.375 + 7.375 = 0.000
0.000 + x = -7.625 + 7.375
x = -7.625 + 7.375

Combine like terms: -7.625 + 7.375 = -0.25
x = -0.25

Simplifying
x = -0.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15, -0.25}

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