16r^2-55r-96=0

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Solution for 16r^2-55r-96=0 equation:


Simplifying
16r2 + -55r + -96 = 0

Reorder the terms:
-96 + -55r + 16r2 = 0

Solving
-96 + -55r + 16r2 = 0

Solving for variable 'r'.

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

Divide each side by '16'.
-6 + -3.4375r + r2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3.4375r + 6 + r2 = 0 + 6

Reorder the terms:
-6 + 6 + -3.4375r + r2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3.4375r + r2 = 0 + 6
-3.4375r + r2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3.4375r + r2 = 6

The r term is -3.4375r.  Take half its coefficient (-1.71875).
Square it (2.954101563) and add it to both sides.

Add '2.954101563' to each side of the equation.
-3.4375r + 2.954101563 + r2 = 6 + 2.954101563

Reorder the terms:
2.954101563 + -3.4375r + r2 = 6 + 2.954101563

Combine like terms: 6 + 2.954101563 = 8.954101563
2.954101563 + -3.4375r + r2 = 8.954101563

Factor a perfect square on the left side:
(r + -1.71875)(r + -1.71875) = 8.954101563

Calculate the square root of the right side: 2.992340482

Break this problem into two subproblems by setting 
(r + -1.71875) equal to 2.992340482 and -2.992340482.

Subproblem 1

r + -1.71875 = 2.992340482 Simplifying r + -1.71875 = 2.992340482 Reorder the terms: -1.71875 + r = 2.992340482 Solving -1.71875 + r = 2.992340482 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + r = 2.992340482 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + r = 2.992340482 + 1.71875 r = 2.992340482 + 1.71875 Combine like terms: 2.992340482 + 1.71875 = 4.711090482 r = 4.711090482 Simplifying r = 4.711090482

Subproblem 2

r + -1.71875 = -2.992340482 Simplifying r + -1.71875 = -2.992340482 Reorder the terms: -1.71875 + r = -2.992340482 Solving -1.71875 + r = -2.992340482 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + r = -2.992340482 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + r = -2.992340482 + 1.71875 r = -2.992340482 + 1.71875 Combine like terms: -2.992340482 + 1.71875 = -1.273590482 r = -1.273590482 Simplifying r = -1.273590482

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.711090482, -1.273590482}

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