-16x^2+60x+6=10

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Solution for -16x^2+60x+6=10 equation: 


Simplifying
-16x2 + 60x + 6 = 10

Reorder the terms:
6 + 60x + -16x2 = 10

Solving
6 + 60x + -16x2 = 10

Solving for variable 'x'.

Reorder the terms:
6 + -10 + 60x + -16x2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + 60x + -16x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + 60x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 15x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 15x + -4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 15x + -4x2 = 0

Solving
-1 + 15x + -4x2 = 0

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

Divide each side by '-4'.
0.25 + -3.75x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -3.75x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -3.75x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -3.75x + x2 = 0 + -0.25
-3.75x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-3.75x + x2 = -0.25

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 = -0.25 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = -0.25 + 3.515625

Combine like terms: -0.25 + 3.515625 = 3.265625
3.515625 + -3.75x + x2 = 3.265625

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 3.265625

Calculate the square root of the right side: 1.807104037

Break this problem into two subproblems by setting 
(x + -1.875) equal to 1.807104037 and -1.807104037.


Subproblem 1
x + -1.875 = 1.807104037

Simplifying
x + -1.875 = 1.807104037

Reorder the terms:
-1.875 + x = 1.807104037

Solving
-1.875 + x = 1.807104037

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 = 1.807104037 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = 1.807104037 + 1.875
x = 1.807104037 + 1.875

Combine like terms: 1.807104037 + 1.875 = 3.682104037
x = 3.682104037

Simplifying
x = 3.682104037


Subproblem 2
x + -1.875 = -1.807104037

Simplifying
x + -1.875 = -1.807104037

Reorder the terms:
-1.875 + x = -1.807104037

Solving
-1.875 + x = -1.807104037

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 = -1.807104037 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = -1.807104037 + 1.875
x = -1.807104037 + 1.875

Combine like terms: -1.807104037 + 1.875 = 0.067895963
x = 0.067895963

Simplifying
x = 0.067895963


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.682104037, 0.067895963}
Solution
x = {3.682104037, 0.067895963}

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