r(r)+10r+12=0

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Solution for r(r)+10r+12=0 equation:


Simplifying
r(r) + 10r + 12 = 0

Multiply r * r
r2 + 10r + 12 = 0

Reorder the terms:
12 + 10r + r2 = 0

Solving
12 + 10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 10r + -12 + r2 = 0 + -12

Reorder the terms:
12 + -12 + 10r + r2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 10r + r2 = 0 + -12
10r + r2 = 0 + -12

Combine like terms: 0 + -12 = -12
10r + r2 = -12

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 = -12 + 25

Reorder the terms:
25 + 10r + r2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + 10r + r2 = 13

Factor a perfect square on the left side:
(r + 5)(r + 5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(r + 5) equal to 3.605551275 and -3.605551275.

Subproblem 1

r + 5 = 3.605551275 Simplifying r + 5 = 3.605551275 Reorder the terms: 5 + r = 3.605551275 Solving 5 + r = 3.605551275 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 = 3.605551275 + -5 Combine like terms: 5 + -5 = 0 0 + r = 3.605551275 + -5 r = 3.605551275 + -5 Combine like terms: 3.605551275 + -5 = -1.394448725 r = -1.394448725 Simplifying r = -1.394448725

Subproblem 2

r + 5 = -3.605551275 Simplifying r + 5 = -3.605551275 Reorder the terms: 5 + r = -3.605551275 Solving 5 + r = -3.605551275 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 = -3.605551275 + -5 Combine like terms: 5 + -5 = 0 0 + r = -3.605551275 + -5 r = -3.605551275 + -5 Combine like terms: -3.605551275 + -5 = -8.605551275 r = -8.605551275 Simplifying r = -8.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-1.394448725, -8.605551275}

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