r^2+2r-7=0

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Solution for r^2+2r-7=0 equation:


Simplifying
r2 + 2r + -7 = 0

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

Solving
-7 + 2r + r2 = 0

Solving for variable 'r'.

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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