-4x^2+39x-10=0

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Solution for -4x^2+39x-10=0 equation: 


Simplifying
-4x2 + 39x + -10 = 0

Reorder the terms:
-10 + 39x + -4x2 = 0

Solving
-10 + 39x + -4x2 = 0

Solving for variable 'x'.

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

Divide each side by '-4'.
2.5 + -9.75x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -9.75x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -9.75x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -9.75x + x2 = 0 + -2.5
-9.75x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-9.75x + x2 = -2.5

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = -2.5 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = -2.5 + 23.765625

Combine like terms: -2.5 + 23.765625 = 21.265625
23.765625 + -9.75x + x2 = 21.265625

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 21.265625

Calculate the square root of the right side: 4.611466686

Break this problem into two subproblems by setting 
(x + -4.875) equal to 4.611466686 and -4.611466686.


Subproblem 1
x + -4.875 = 4.611466686

Simplifying
x + -4.875 = 4.611466686

Reorder the terms:
-4.875 + x = 4.611466686

Solving
-4.875 + x = 4.611466686

Solving for variable 'x'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = 4.611466686 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = 4.611466686 + 4.875
x = 4.611466686 + 4.875

Combine like terms: 4.611466686 + 4.875 = 9.486466686
x = 9.486466686

Simplifying
x = 9.486466686


Subproblem 2
x + -4.875 = -4.611466686

Simplifying
x + -4.875 = -4.611466686

Reorder the terms:
-4.875 + x = -4.611466686

Solving
-4.875 + x = -4.611466686

Solving for variable 'x'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = -4.611466686 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = -4.611466686 + 4.875
x = -4.611466686 + 4.875

Combine like terms: -4.611466686 + 4.875 = 0.263533314
x = 0.263533314

Simplifying
x = 0.263533314


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.486466686, 0.263533314}

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