3r^2+9r-4=0

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Solution for 3r^2+9r-4=0 equation:


Simplifying
3r2 + 9r + -4 = 0

Reorder the terms:
-4 + 9r + 3r2 = 0

Solving
-4 + 9r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
-1.333333333 + 3r + r2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 3r + 1.333333333 + r2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 3r + r2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 3r + r2 = 0 + 1.333333333
3r + r2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
3r + r2 = 1.333333333

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 1.333333333 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 1.333333333 + 2.25

Combine like terms: 1.333333333 + 2.25 = 3.583333333
2.25 + 3r + r2 = 3.583333333

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(r + 1.5) equal to 1.892969449 and -1.892969449.

Subproblem 1

r + 1.5 = 1.892969449 Simplifying r + 1.5 = 1.892969449 Reorder the terms: 1.5 + r = 1.892969449 Solving 1.5 + r = 1.892969449 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = 1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 1.892969449 + -1.5 r = 1.892969449 + -1.5 Combine like terms: 1.892969449 + -1.5 = 0.392969449 r = 0.392969449 Simplifying r = 0.392969449

Subproblem 2

r + 1.5 = -1.892969449 Simplifying r + 1.5 = -1.892969449 Reorder the terms: 1.5 + r = -1.892969449 Solving 1.5 + r = -1.892969449 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = -1.892969449 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -1.892969449 + -1.5 r = -1.892969449 + -1.5 Combine like terms: -1.892969449 + -1.5 = -3.392969449 r = -3.392969449 Simplifying r = -3.392969449

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.392969449, -3.392969449}

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