5r^2-18r+10=0

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Solution for 5r^2-18r+10=0 equation:


Simplifying
5r2 + -18r + 10 = 0

Reorder the terms:
10 + -18r + 5r2 = 0

Solving
10 + -18r + 5r2 = 0

Solving for variable 'r'.

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

Divide each side by '5'.
2 + -3.6r + r2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.6r + -2 + r2 = 0 + -2

Reorder the terms:
2 + -2 + -3.6r + r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.6r + r2 = 0 + -2
-3.6r + r2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.6r + r2 = -2

The r term is -3.6r.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6r + 3.24 + r2 = -2 + 3.24

Reorder the terms:
3.24 + -3.6r + r2 = -2 + 3.24

Combine like terms: -2 + 3.24 = 1.24
3.24 + -3.6r + r2 = 1.24

Factor a perfect square on the left side:
(r + -1.8)(r + -1.8) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(r + -1.8) equal to 1.113552873 and -1.113552873.

Subproblem 1

r + -1.8 = 1.113552873 Simplifying r + -1.8 = 1.113552873 Reorder the terms: -1.8 + r = 1.113552873 Solving -1.8 + r = 1.113552873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + r = 1.113552873 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + r = 1.113552873 + 1.8 r = 1.113552873 + 1.8 Combine like terms: 1.113552873 + 1.8 = 2.913552873 r = 2.913552873 Simplifying r = 2.913552873

Subproblem 2

r + -1.8 = -1.113552873 Simplifying r + -1.8 = -1.113552873 Reorder the terms: -1.8 + r = -1.113552873 Solving -1.8 + r = -1.113552873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + r = -1.113552873 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + r = -1.113552873 + 1.8 r = -1.113552873 + 1.8 Combine like terms: -1.113552873 + 1.8 = 0.686447127 r = 0.686447127 Simplifying r = 0.686447127

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.913552873, 0.686447127}

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