r^2+10r=-7

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Solution for r^2+10r=-7 equation:


Simplifying
r2 + 10r = -7

Reorder the terms:
10r + r2 = -7

Solving
10r + r2 = -7

Solving for variable 'r'.

Reorder the terms:
7 + 10r + r2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 10r + -7 + r2 = 0 + -7

Reorder the terms:
7 + -7 + 10r + r2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 10r + r2 = 0 + -7
10r + r2 = 0 + -7

Combine like terms: 0 + -7 = -7
10r + r2 = -7

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 = -7 + 25

Reorder the terms:
25 + 10r + r2 = -7 + 25

Combine like terms: -7 + 25 = 18
25 + 10r + r2 = 18

Factor a perfect square on the left side:
(r + 5)(r + 5) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(r + 5) equal to 4.242640687 and -4.242640687.

Subproblem 1

r + 5 = 4.242640687 Simplifying r + 5 = 4.242640687 Reorder the terms: 5 + r = 4.242640687 Solving 5 + r = 4.242640687 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 = 4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + r = 4.242640687 + -5 r = 4.242640687 + -5 Combine like terms: 4.242640687 + -5 = -0.757359313 r = -0.757359313 Simplifying r = -0.757359313

Subproblem 2

r + 5 = -4.242640687 Simplifying r + 5 = -4.242640687 Reorder the terms: 5 + r = -4.242640687 Solving 5 + r = -4.242640687 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 = -4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + r = -4.242640687 + -5 r = -4.242640687 + -5 Combine like terms: -4.242640687 + -5 = -9.242640687 r = -9.242640687 Simplifying r = -9.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.757359313, -9.242640687}

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