8r^2-3r-12=6

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Solution for 8r^2-3r-12=6 equation:


Simplifying
8r2 + -3r + -12 = 6

Reorder the terms:
-12 + -3r + 8r2 = 6

Solving
-12 + -3r + 8r2 = 6

Solving for variable 'r'.

Reorder the terms:
-12 + -6 + -3r + 8r2 = 6 + -6

Combine like terms: -12 + -6 = -18
-18 + -3r + 8r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-18 + -3r + 8r2 = 0

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

Divide each side by '8'.
-2.25 + -0.375r + r2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.375r + 2.25 + r2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.375r + r2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.375r + r2 = 0 + 2.25
-0.375r + r2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.375r + r2 = 2.25

The r term is -0.375r.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375r + 0.03515625 + r2 = 2.25 + 0.03515625

Reorder the terms:
0.03515625 + -0.375r + r2 = 2.25 + 0.03515625

Combine like terms: 2.25 + 0.03515625 = 2.28515625
0.03515625 + -0.375r + r2 = 2.28515625

Factor a perfect square on the left side:
(r + -0.1875)(r + -0.1875) = 2.28515625

Calculate the square root of the right side: 1.511673328

Break this problem into two subproblems by setting 
(r + -0.1875) equal to 1.511673328 and -1.511673328.

Subproblem 1

r + -0.1875 = 1.511673328 Simplifying r + -0.1875 = 1.511673328 Reorder the terms: -0.1875 + r = 1.511673328 Solving -0.1875 + r = 1.511673328 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + r = 1.511673328 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + r = 1.511673328 + 0.1875 r = 1.511673328 + 0.1875 Combine like terms: 1.511673328 + 0.1875 = 1.699173328 r = 1.699173328 Simplifying r = 1.699173328

Subproblem 2

r + -0.1875 = -1.511673328 Simplifying r + -0.1875 = -1.511673328 Reorder the terms: -0.1875 + r = -1.511673328 Solving -0.1875 + r = -1.511673328 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + r = -1.511673328 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + r = -1.511673328 + 0.1875 r = -1.511673328 + 0.1875 Combine like terms: -1.511673328 + 0.1875 = -1.324173328 r = -1.324173328 Simplifying r = -1.324173328

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.699173328, -1.324173328}

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