-16x^2+68x=4.25

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Solution for -16x^2+68x=4.25 equation: 


Simplifying
-16x2 + 68x = 4.25

Reorder the terms:
68x + -16x2 = 4.25

Solving
68x + -16x2 = 4.25

Solving for variable 'x'.

Reorder the terms:
-4.25 + 68x + -16x2 = 4.25 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
-4.25 + 68x + -16x2 = 0.00

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

Divide each side by '-16'.
0.265625 + -4.25x + x2 = 0.00

Move the constant term to the right:

Add '-0.265625' to each side of the equation.
0.265625 + -4.25x + -0.265625 + x2 = 0.00 + -0.265625

Reorder the terms:
0.265625 + -0.265625 + -4.25x + x2 = 0.00 + -0.265625

Combine like terms: 0.265625 + -0.265625 = 0.000000
0.000000 + -4.25x + x2 = 0.00 + -0.265625
-4.25x + x2 = 0.00 + -0.265625

Combine like terms: 0.00 + -0.265625 = -0.265625
-4.25x + x2 = -0.265625

The x term is -4.25x.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x + 4.515625 + x2 = -0.265625 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = -0.265625 + 4.515625

Combine like terms: -0.265625 + 4.515625 = 4.25
4.515625 + -4.25x + x2 = 4.25

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -2.125) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + -2.125 = 2.061552813

Simplifying
x + -2.125 = 2.061552813

Reorder the terms:
-2.125 + x = 2.061552813

Solving
-2.125 + x = 2.061552813

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = 2.061552813 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = 2.061552813 + 2.125
x = 2.061552813 + 2.125

Combine like terms: 2.061552813 + 2.125 = 4.186552813
x = 4.186552813

Simplifying
x = 4.186552813


Subproblem 2
x + -2.125 = -2.061552813

Simplifying
x + -2.125 = -2.061552813

Reorder the terms:
-2.125 + x = -2.061552813

Solving
-2.125 + x = -2.061552813

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = -2.061552813 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = -2.061552813 + 2.125
x = -2.061552813 + 2.125

Combine like terms: -2.061552813 + 2.125 = 0.063447187
x = 0.063447187

Simplifying
x = 0.063447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.186552813, 0.063447187}

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