20r^2+5r-4=0

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Solution for 20r^2+5r-4=0 equation:


Simplifying
20r2 + 5r + -4 = 0

Reorder the terms:
-4 + 5r + 20r2 = 0

Solving
-4 + 5r + 20r2 = 0

Solving for variable 'r'.

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

Divide each side by '20'.
-0.2 + 0.25r + r2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.25r + 0.2 + r2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.25r + r2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.25r + r2 = 0 + 0.2
0.25r + r2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.25r + r2 = 0.2

The r term is 0.25r.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25r + 0.015625 + r2 = 0.2 + 0.015625

Reorder the terms:
0.015625 + 0.25r + r2 = 0.2 + 0.015625

Combine like terms: 0.2 + 0.015625 = 0.215625
0.015625 + 0.25r + r2 = 0.215625

Factor a perfect square on the left side:
(r + 0.125)(r + 0.125) = 0.215625

Calculate the square root of the right side: 0.464354391

Break this problem into two subproblems by setting 
(r + 0.125) equal to 0.464354391 and -0.464354391.

Subproblem 1

r + 0.125 = 0.464354391 Simplifying r + 0.125 = 0.464354391 Reorder the terms: 0.125 + r = 0.464354391 Solving 0.125 + r = 0.464354391 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + r = 0.464354391 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + r = 0.464354391 + -0.125 r = 0.464354391 + -0.125 Combine like terms: 0.464354391 + -0.125 = 0.339354391 r = 0.339354391 Simplifying r = 0.339354391

Subproblem 2

r + 0.125 = -0.464354391 Simplifying r + 0.125 = -0.464354391 Reorder the terms: 0.125 + r = -0.464354391 Solving 0.125 + r = -0.464354391 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + r = -0.464354391 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + r = -0.464354391 + -0.125 r = -0.464354391 + -0.125 Combine like terms: -0.464354391 + -0.125 = -0.589354391 r = -0.589354391 Simplifying r = -0.589354391

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.339354391, -0.589354391}

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