r^2+8r=21

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Solution for r^2+8r=21 equation:


Simplifying
r2 + 8r = 21

Reorder the terms:
8r + r2 = 21

Solving
8r + r2 = 21

Solving for variable 'r'.

Reorder the terms:
-21 + 8r + r2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 8r + 21 + r2 = 0 + 21

Reorder the terms:
-21 + 21 + 8r + r2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 8r + r2 = 0 + 21
8r + r2 = 0 + 21

Combine like terms: 0 + 21 = 21
8r + r2 = 21

The r term is 8r.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r + 16 + r2 = 21 + 16

Reorder the terms:
16 + 8r + r2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + 8r + r2 = 37

Factor a perfect square on the left side:
(r + 4)(r + 4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(r + 4) equal to 6.08276253 and -6.08276253.

Subproblem 1

r + 4 = 6.08276253 Simplifying r + 4 = 6.08276253 Reorder the terms: 4 + r = 6.08276253 Solving 4 + r = 6.08276253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + r = 6.08276253 + -4 r = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 r = 2.08276253 Simplifying r = 2.08276253

Subproblem 2

r + 4 = -6.08276253 Simplifying r + 4 = -6.08276253 Reorder the terms: 4 + r = -6.08276253 Solving 4 + r = -6.08276253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + r = -6.08276253 + -4 r = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 r = -10.08276253 Simplifying r = -10.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.08276253, -10.08276253}

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