14x-4x^2=6.25

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Solution for 14x-4x^2=6.25 equation: 


Simplifying
14x + -4x2 = 6.25

Solving
14x + -4x2 = 6.25

Solving for variable 'x'.

Reorder the terms:
-6.25 + 14x + -4x2 = 6.25 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
-6.25 + 14x + -4x2 = 0.00

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1.5625 + -3.5x + x2 = 0.00

Move the constant term to the right:

Add '-1.5625' to each side of the equation.
1.5625 + -3.5x + -1.5625 + x2 = 0.00 + -1.5625

Reorder the terms:
1.5625 + -1.5625 + -3.5x + x2 = 0.00 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + -3.5x + x2 = 0.00 + -1.5625
-3.5x + x2 = 0.00 + -1.5625

Combine like terms: 0.00 + -1.5625 = -1.5625
-3.5x + x2 = -1.5625

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -1.5625 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -1.5625 + 3.0625

Combine like terms: -1.5625 + 3.0625 = 1.5
3.0625 + -3.5x + x2 = 1.5

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.224744871 and -1.224744871.


Subproblem 1
x + -1.75 = 1.224744871

Simplifying
x + -1.75 = 1.224744871

Reorder the terms:
-1.75 + x = 1.224744871

Solving
-1.75 + x = 1.224744871

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 1.224744871 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 1.224744871 + 1.75
x = 1.224744871 + 1.75

Combine like terms: 1.224744871 + 1.75 = 2.974744871
x = 2.974744871

Simplifying
x = 2.974744871


Subproblem 2
x + -1.75 = -1.224744871

Simplifying
x + -1.75 = -1.224744871

Reorder the terms:
-1.75 + x = -1.224744871

Solving
-1.75 + x = -1.224744871

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -1.224744871 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -1.224744871 + 1.75
x = -1.224744871 + 1.75

Combine like terms: -1.224744871 + 1.75 = 0.525255129
x = 0.525255129

Simplifying
x = 0.525255129


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.974744871, 0.525255129}

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