-16x^2+66x+13=0

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Solution for -16x^2+66x+13=0 equation:


Simplifying
-16x2 + 66x + 13 = 0

Reorder the terms:
13 + 66x + -16x2 = 0

Solving
13 + 66x + -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'.
-0.8125 + -4.125x + x2 = 0

Move the constant term to the right:

Add '0.8125' to each side of the equation.
-0.8125 + -4.125x + 0.8125 + x2 = 0 + 0.8125

Reorder the terms:
-0.8125 + 0.8125 + -4.125x + x2 = 0 + 0.8125

Combine like terms: -0.8125 + 0.8125 = 0.0000
0.0000 + -4.125x + x2 = 0 + 0.8125
-4.125x + x2 = 0 + 0.8125

Combine like terms: 0 + 0.8125 = 0.8125
-4.125x + x2 = 0.8125

The x term is -4.125x.  Take half its coefficient (-2.0625).
Square it (4.25390625) and add it to both sides.

Add '4.25390625' to each side of the equation.
-4.125x + 4.25390625 + x2 = 0.8125 + 4.25390625

Reorder the terms:
4.25390625 + -4.125x + x2 = 0.8125 + 4.25390625

Combine like terms: 0.8125 + 4.25390625 = 5.06640625
4.25390625 + -4.125x + x2 = 5.06640625

Factor a perfect square on the left side:
(x + -2.0625)(x + -2.0625) = 5.06640625

Calculate the square root of the right side: 2.250867888

Break this problem into two subproblems by setting 
(x + -2.0625) equal to 2.250867888 and -2.250867888.

Subproblem 1

x + -2.0625 = 2.250867888 Simplifying x + -2.0625 = 2.250867888 Reorder the terms: -2.0625 + x = 2.250867888 Solving -2.0625 + x = 2.250867888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = 2.250867888 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = 2.250867888 + 2.0625 x = 2.250867888 + 2.0625 Combine like terms: 2.250867888 + 2.0625 = 4.313367888 x = 4.313367888 Simplifying x = 4.313367888

Subproblem 2

x + -2.0625 = -2.250867888 Simplifying x + -2.0625 = -2.250867888 Reorder the terms: -2.0625 + x = -2.250867888 Solving -2.0625 + x = -2.250867888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = -2.250867888 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = -2.250867888 + 2.0625 x = -2.250867888 + 2.0625 Combine like terms: -2.250867888 + 2.0625 = -0.188367888 x = -0.188367888 Simplifying x = -0.188367888

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.313367888, -0.188367888}

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