r^2+4r+4=7

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Solution for r^2+4r+4=7 equation:


Simplifying
r2 + 4r + 4 = 7

Reorder the terms:
4 + 4r + r2 = 7

Solving
4 + 4r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
4 + -7 + 4r + r2 = 7 + -7

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

Combine like terms: 7 + -7 = 0
-3 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 4r + 3 + r2 = 0 + 3

Reorder the terms:
-3 + 3 + 4r + r2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4r + r2 = 0 + 3
4r + r2 = 0 + 3

Combine like terms: 0 + 3 = 3
4r + r2 = 3

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = 3 + 4

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

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

Factor a perfect square on the left side:
(r + 2)(r + 2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(r + 2) equal to 2.645751311 and -2.645751311.

Subproblem 1

r + 2 = 2.645751311 Simplifying r + 2 = 2.645751311 Reorder the terms: 2 + r = 2.645751311 Solving 2 + r = 2.645751311 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + r = 2.645751311 + -2 r = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 r = 0.645751311 Simplifying r = 0.645751311

Subproblem 2

r + 2 = -2.645751311 Simplifying r + 2 = -2.645751311 Reorder the terms: 2 + r = -2.645751311 Solving 2 + r = -2.645751311 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + r = -2.645751311 + -2 r = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 r = -4.645751311 Simplifying r = -4.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.645751311, -4.645751311}

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