r^2+2r-3=4

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Solution for r^2+2r-3=4 equation: 


Simplifying
r2 + 2r + -3 = 4

Reorder the terms:
-3 + 2r + r2 = 4

Solving
-3 + 2r + r2 = 4

Solving for variable 'r'.

Reorder the terms:
-3 + -4 + 2r + r2 = 4 + -4

Combine like terms: -3 + -4 = -7
-7 + 2r + r2 = 4 + -4

Combine like terms: 4 + -4 = 0
-7 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 2r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + 2r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2r + r2 = 0 + 7
2r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
2r + r2 = 7

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 = 7 + 1

Reorder the terms:
1 + 2r + r2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + 2r + r2 = 8

Factor a perfect square on the left side:
(r + 1)(r + 1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(r + 1) equal to 2.828427125 and -2.828427125.


Subproblem 1
r + 1 = 2.828427125

Simplifying
r + 1 = 2.828427125

Reorder the terms:
1 + r = 2.828427125

Solving
1 + r = 2.828427125

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 = 2.828427125 + -1

Combine like terms: 1 + -1 = 0
0 + r = 2.828427125 + -1
r = 2.828427125 + -1

Combine like terms: 2.828427125 + -1 = 1.828427125
r = 1.828427125

Simplifying
r = 1.828427125


Subproblem 2
r + 1 = -2.828427125

Simplifying
r + 1 = -2.828427125

Reorder the terms:
1 + r = -2.828427125

Solving
1 + r = -2.828427125

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 = -2.828427125 + -1

Combine like terms: 1 + -1 = 0
0 + r = -2.828427125 + -1
r = -2.828427125 + -1

Combine like terms: -2.828427125 + -1 = -3.828427125
r = -3.828427125

Simplifying
r = -3.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.828427125, -3.828427125}

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