r^2+1.5r-20=0

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Solution for r^2+1.5r-20=0 equation:


Simplifying
r2 + 1.5r + -20 = 0

Reorder the terms:
-20 + 1.5r + r2 = 0

Solving
-20 + 1.5r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 1.5r + 20 + r2 = 0 + 20

Reorder the terms:
-20 + 20 + 1.5r + r2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 1.5r + r2 = 0 + 20
1.5r + r2 = 0 + 20

Combine like terms: 0 + 20 = 20
1.5r + r2 = 20

The r term is 1.5r.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5r + 0.5625 + r2 = 20 + 0.5625

Reorder the terms:
0.5625 + 1.5r + r2 = 20 + 0.5625

Combine like terms: 20 + 0.5625 = 20.5625
0.5625 + 1.5r + r2 = 20.5625

Factor a perfect square on the left side:
(r + 0.75)(r + 0.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(r + 0.75) equal to 4.534589287 and -4.534589287.

Subproblem 1

r + 0.75 = 4.534589287 Simplifying r + 0.75 = 4.534589287 Reorder the terms: 0.75 + r = 4.534589287 Solving 0.75 + r = 4.534589287 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = 4.534589287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = 4.534589287 + -0.75 r = 4.534589287 + -0.75 Combine like terms: 4.534589287 + -0.75 = 3.784589287 r = 3.784589287 Simplifying r = 3.784589287

Subproblem 2

r + 0.75 = -4.534589287 Simplifying r + 0.75 = -4.534589287 Reorder the terms: 0.75 + r = -4.534589287 Solving 0.75 + r = -4.534589287 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = -4.534589287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = -4.534589287 + -0.75 r = -4.534589287 + -0.75 Combine like terms: -4.534589287 + -0.75 = -5.284589287 r = -5.284589287 Simplifying r = -5.284589287

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.784589287, -5.284589287}

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