8r^2+3r-30=0

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Solution for 8r^2+3r-30=0 equation:


Simplifying
8r2 + 3r + -30 = 0

Reorder the terms:
-30 + 3r + 8r2 = 0

Solving
-30 + 3r + 8r2 = 0

Solving for variable 'r'.

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

Divide each side by '8'.
-3.75 + 0.375r + r2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 0.375r + 3.75 + r2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 0.375r + r2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 0.375r + r2 = 0 + 3.75
0.375r + r2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
0.375r + r2 = 3.75

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 = 3.75 + 0.03515625

Reorder the terms:
0.03515625 + 0.375r + r2 = 3.75 + 0.03515625

Combine like terms: 3.75 + 0.03515625 = 3.78515625
0.03515625 + 0.375r + r2 = 3.78515625

Factor a perfect square on the left side:
(r + 0.1875)(r + 0.1875) = 3.78515625

Calculate the square root of the right side: 1.945547802

Break this problem into two subproblems by setting 
(r + 0.1875) equal to 1.945547802 and -1.945547802.

Subproblem 1

r + 0.1875 = 1.945547802 Simplifying r + 0.1875 = 1.945547802 Reorder the terms: 0.1875 + r = 1.945547802 Solving 0.1875 + r = 1.945547802 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 = 1.945547802 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + r = 1.945547802 + -0.1875 r = 1.945547802 + -0.1875 Combine like terms: 1.945547802 + -0.1875 = 1.758047802 r = 1.758047802 Simplifying r = 1.758047802

Subproblem 2

r + 0.1875 = -1.945547802 Simplifying r + 0.1875 = -1.945547802 Reorder the terms: 0.1875 + r = -1.945547802 Solving 0.1875 + r = -1.945547802 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 = -1.945547802 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + r = -1.945547802 + -0.1875 r = -1.945547802 + -0.1875 Combine like terms: -1.945547802 + -0.1875 = -2.133047802 r = -2.133047802 Simplifying r = -2.133047802

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.758047802, -2.133047802}

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