r^2+2r-10=0

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Solution for r^2+2r-10=0 equation:


Simplifying
r2 + 2r + -10 = 0

Reorder the terms:
-10 + 2r + r2 = 0

Solving
-10 + 2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2r + 10 + r2 = 0 + 10

Reorder the terms:
-10 + 10 + 2r + r2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2r + r2 = 0 + 10
2r + r2 = 0 + 10

Combine like terms: 0 + 10 = 10
2r + r2 = 10

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 10 + 1

Reorder the terms:
1 + 2r + r2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + 2r + r2 = 11

Factor a perfect square on the left side:
(r + 1)(r + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(r + 1) equal to 3.31662479 and -3.31662479.

Subproblem 1

r + 1 = 3.31662479 Simplifying r + 1 = 3.31662479 Reorder the terms: 1 + r = 3.31662479 Solving 1 + r = 3.31662479 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + r = 3.31662479 + -1 r = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 r = 2.31662479 Simplifying r = 2.31662479

Subproblem 2

r + 1 = -3.31662479 Simplifying r + 1 = -3.31662479 Reorder the terms: 1 + r = -3.31662479 Solving 1 + r = -3.31662479 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + r = -3.31662479 + -1 r = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 r = -4.31662479 Simplifying r = -4.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.31662479, -4.31662479}

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