16x^2-60x+56.25=0

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Solution for 16x^2-60x+56.25=0 equation:


Simplifying
16x2 + -60x + 56.25 = 0

Reorder the terms:
56.25 + -60x + 16x2 = 0

Solving
56.25 + -60x + 16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
3.515625 + -3.75x + x2 = 0

Move the constant term to the right:

Add '-3.515625' to each side of the equation.
3.515625 + -3.75x + -3.515625 + x2 = 0 + -3.515625

Reorder the terms:
3.515625 + -3.515625 + -3.75x + x2 = 0 + -3.515625

Combine like terms: 3.515625 + -3.515625 = 0.000000
0.000000 + -3.75x + x2 = 0 + -3.515625
-3.75x + x2 = 0 + -3.515625

Combine like terms: 0 + -3.515625 = -3.515625
-3.75x + x2 = -3.515625

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = -3.515625 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = -3.515625 + 3.515625

Combine like terms: -3.515625 + 3.515625 = 0.000000
3.515625 + -3.75x + x2 = 0.000000

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 0.000000

Calculate the square root of the right side: 0.000000

Break this problem into two subproblems by setting 
(x + -1.875) equal to 0.000000 and 0.000000.

Subproblem 1

x + -1.875 = 0.000000 Simplifying x + -1.875 = 0.000000 Reorder the terms: -1.875 + x = 0.000000 Solving -1.875 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 0.000000 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 0.000000 + 1.875 x = 0.000000 + 1.875 Combine like terms: 0.000000 + 1.875 = 1.875 x = 1.875 Simplifying x = 1.875

Subproblem 2

x + -1.875 = 0.000000 Simplifying x + -1.875 = 0.000000 Reorder the terms: -1.875 + x = 0.000000 Solving -1.875 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 0.000000 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 0.000000 + 1.875 x = 0.000000 + 1.875 Combine like terms: 0.000000 + 1.875 = 1.875 x = 1.875 Simplifying x = 1.875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.875, 1.875}

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