r^2+10r=-22

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Solution for r^2+10r=-22 equation:


Simplifying
r2 + 10r = -22

Reorder the terms:
10r + r2 = -22

Solving
10r + r2 = -22

Solving for variable 'r'.

Reorder the terms:
22 + 10r + r2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + 10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 10r + -22 + r2 = 0 + -22

Reorder the terms:
22 + -22 + 10r + r2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 10r + r2 = 0 + -22
10r + r2 = 0 + -22

Combine like terms: 0 + -22 = -22
10r + r2 = -22

The r term is 10r.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10r + 25 + r2 = -22 + 25

Reorder the terms:
25 + 10r + r2 = -22 + 25

Combine like terms: -22 + 25 = 3
25 + 10r + r2 = 3

Factor a perfect square on the left side:
(r + 5)(r + 5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(r + 5) equal to 1.732050808 and -1.732050808.

Subproblem 1

r + 5 = 1.732050808 Simplifying r + 5 = 1.732050808 Reorder the terms: 5 + r = 1.732050808 Solving 5 + r = 1.732050808 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + r = 1.732050808 + -5 r = 1.732050808 + -5 Combine like terms: 1.732050808 + -5 = -3.267949192 r = -3.267949192 Simplifying r = -3.267949192

Subproblem 2

r + 5 = -1.732050808 Simplifying r + 5 = -1.732050808 Reorder the terms: 5 + r = -1.732050808 Solving 5 + r = -1.732050808 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + r = -1.732050808 + -5 r = -1.732050808 + -5 Combine like terms: -1.732050808 + -5 = -6.732050808 r = -6.732050808 Simplifying r = -6.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-3.267949192, -6.732050808}

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