x^2-15.75x+6.4375=0

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Solution for x^2-15.75x+6.4375=0 equation: 


Simplifying
x2 + -15.75x + 6.4375 = 0

Reorder the terms:
6.4375 + -15.75x + x2 = 0

Solving
6.4375 + -15.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6.4375' to each side of the equation.
6.4375 + -15.75x + -6.4375 + x2 = 0 + -6.4375

Reorder the terms:
6.4375 + -6.4375 + -15.75x + x2 = 0 + -6.4375

Combine like terms: 6.4375 + -6.4375 = 0.0000
0.0000 + -15.75x + x2 = 0 + -6.4375
-15.75x + x2 = 0 + -6.4375

Combine like terms: 0 + -6.4375 = -6.4375
-15.75x + x2 = -6.4375

The x term is -15.75x.  Take half its coefficient (-7.875).
Square it (62.015625) and add it to both sides.

Add '62.015625' to each side of the equation.
-15.75x + 62.015625 + x2 = -6.4375 + 62.015625

Reorder the terms:
62.015625 + -15.75x + x2 = -6.4375 + 62.015625

Combine like terms: -6.4375 + 62.015625 = 55.578125
62.015625 + -15.75x + x2 = 55.578125

Factor a perfect square on the left side:
(x + -7.875)(x + -7.875) = 55.578125

Calculate the square root of the right side: 7.455073776

Break this problem into two subproblems by setting 
(x + -7.875) equal to 7.455073776 and -7.455073776.


Subproblem 1
x + -7.875 = 7.455073776

Simplifying
x + -7.875 = 7.455073776

Reorder the terms:
-7.875 + x = 7.455073776

Solving
-7.875 + x = 7.455073776

Solving for variable 'x'.

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

Add '7.875' to each side of the equation.
-7.875 + 7.875 + x = 7.455073776 + 7.875

Combine like terms: -7.875 + 7.875 = 0.000
0.000 + x = 7.455073776 + 7.875
x = 7.455073776 + 7.875

Combine like terms: 7.455073776 + 7.875 = 15.330073776
x = 15.330073776

Simplifying
x = 15.330073776


Subproblem 2
x + -7.875 = -7.455073776

Simplifying
x + -7.875 = -7.455073776

Reorder the terms:
-7.875 + x = -7.455073776

Solving
-7.875 + x = -7.455073776

Solving for variable 'x'.

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

Add '7.875' to each side of the equation.
-7.875 + 7.875 + x = -7.455073776 + 7.875

Combine like terms: -7.875 + 7.875 = 0.000
0.000 + x = -7.455073776 + 7.875
x = -7.455073776 + 7.875

Combine like terms: -7.455073776 + 7.875 = 0.419926224
x = 0.419926224

Simplifying
x = 0.419926224


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.330073776, 0.419926224}

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