-16x^2+27x-10=0

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Solution for -16x^2+27x-10=0 equation: 


Simplifying
-16x2 + 27x + -10 = 0

Reorder the terms:
-10 + 27x + -16x2 = 0

Solving
-10 + 27x + -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'.
0.625 + -1.6875x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -1.6875x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -1.6875x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -1.6875x + x2 = 0 + -0.625
-1.6875x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-1.6875x + x2 = -0.625

The x term is -1.6875x.  Take half its coefficient (-0.84375).
Square it (0.7119140625) and add it to both sides.

Add '0.7119140625' to each side of the equation.
-1.6875x + 0.7119140625 + x2 = -0.625 + 0.7119140625

Reorder the terms:
0.7119140625 + -1.6875x + x2 = -0.625 + 0.7119140625

Combine like terms: -0.625 + 0.7119140625 = 0.0869140625
0.7119140625 + -1.6875x + x2 = 0.0869140625

Factor a perfect square on the left side:
(x + -0.84375)(x + -0.84375) = 0.0869140625

Calculate the square root of the right side: 0.29481191

Break this problem into two subproblems by setting 
(x + -0.84375) equal to 0.29481191 and -0.29481191.


Subproblem 1
x + -0.84375 = 0.29481191

Simplifying
x + -0.84375 = 0.29481191

Reorder the terms:
-0.84375 + x = 0.29481191

Solving
-0.84375 + x = 0.29481191

Solving for variable 'x'.

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

Add '0.84375' to each side of the equation.
-0.84375 + 0.84375 + x = 0.29481191 + 0.84375

Combine like terms: -0.84375 + 0.84375 = 0.00000
0.00000 + x = 0.29481191 + 0.84375
x = 0.29481191 + 0.84375

Combine like terms: 0.29481191 + 0.84375 = 1.13856191
x = 1.13856191

Simplifying
x = 1.13856191


Subproblem 2
x + -0.84375 = -0.29481191

Simplifying
x + -0.84375 = -0.29481191

Reorder the terms:
-0.84375 + x = -0.29481191

Solving
-0.84375 + x = -0.29481191

Solving for variable 'x'.

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

Add '0.84375' to each side of the equation.
-0.84375 + 0.84375 + x = -0.29481191 + 0.84375

Combine like terms: -0.84375 + 0.84375 = 0.00000
0.00000 + x = -0.29481191 + 0.84375
x = -0.29481191 + 0.84375

Combine like terms: -0.29481191 + 0.84375 = 0.54893809
x = 0.54893809

Simplifying
x = 0.54893809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.13856191, 0.54893809}

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