r^2=18r-7

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Solution for r^2=18r-7 equation:


Simplifying
r2 = 18r + -7

Reorder the terms:
r2 = -7 + 18r

Solving
r2 = -7 + 18r

Solving for variable 'r'.

Reorder the terms:
7 + -18r + r2 = -7 + 18r + 7 + -18r

Reorder the terms:
7 + -18r + r2 = -7 + 7 + 18r + -18r

Combine like terms: -7 + 7 = 0
7 + -18r + r2 = 0 + 18r + -18r
7 + -18r + r2 = 18r + -18r

Combine like terms: 18r + -18r = 0
7 + -18r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -18r + -7 + r2 = 0 + -7

Reorder the terms:
7 + -7 + -18r + r2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -18r + r2 = 0 + -7
-18r + r2 = 0 + -7

Combine like terms: 0 + -7 = -7
-18r + r2 = -7

The r term is -18r.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18r + 81 + r2 = -7 + 81

Reorder the terms:
81 + -18r + r2 = -7 + 81

Combine like terms: -7 + 81 = 74
81 + -18r + r2 = 74

Factor a perfect square on the left side:
(r + -9)(r + -9) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(r + -9) equal to 8.602325267 and -8.602325267.

Subproblem 1

r + -9 = 8.602325267 Simplifying r + -9 = 8.602325267 Reorder the terms: -9 + r = 8.602325267 Solving -9 + r = 8.602325267 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + r = 8.602325267 + 9 Combine like terms: -9 + 9 = 0 0 + r = 8.602325267 + 9 r = 8.602325267 + 9 Combine like terms: 8.602325267 + 9 = 17.602325267 r = 17.602325267 Simplifying r = 17.602325267

Subproblem 2

r + -9 = -8.602325267 Simplifying r + -9 = -8.602325267 Reorder the terms: -9 + r = -8.602325267 Solving -9 + r = -8.602325267 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + r = -8.602325267 + 9 Combine like terms: -9 + 9 = 0 0 + r = -8.602325267 + 9 r = -8.602325267 + 9 Combine like terms: -8.602325267 + 9 = 0.397674733 r = 0.397674733 Simplifying r = 0.397674733

Solution

The solution to the problem is based on the solutions from the subproblems. r = {17.602325267, 0.397674733}

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