g^2+4g=47

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Solution for g^2+4g=47 equation:


Simplifying
g2 + 4g = 47

Reorder the terms:
4g + g2 = 47

Solving
4g + g2 = 47

Solving for variable 'g'.

Reorder the terms:
-47 + 4g + g2 = 47 + -47

Combine like terms: 47 + -47 = 0
-47 + 4g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + 4g + 47 + g2 = 0 + 47

Reorder the terms:
-47 + 47 + 4g + g2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 4g + g2 = 0 + 47
4g + g2 = 0 + 47

Combine like terms: 0 + 47 = 47
4g + g2 = 47

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

Add '4' to each side of the equation.
4g + 4 + g2 = 47 + 4

Reorder the terms:
4 + 4g + g2 = 47 + 4

Combine like terms: 47 + 4 = 51
4 + 4g + g2 = 51

Factor a perfect square on the left side:
(g + 2)(g + 2) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(g + 2) equal to 7.141428429 and -7.141428429.

Subproblem 1

g + 2 = 7.141428429 Simplifying g + 2 = 7.141428429 Reorder the terms: 2 + g = 7.141428429 Solving 2 + g = 7.141428429 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + g = 7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + g = 7.141428429 + -2 g = 7.141428429 + -2 Combine like terms: 7.141428429 + -2 = 5.141428429 g = 5.141428429 Simplifying g = 5.141428429

Subproblem 2

g + 2 = -7.141428429 Simplifying g + 2 = -7.141428429 Reorder the terms: 2 + g = -7.141428429 Solving 2 + g = -7.141428429 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + g = -7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + g = -7.141428429 + -2 g = -7.141428429 + -2 Combine like terms: -7.141428429 + -2 = -9.141428429 g = -9.141428429 Simplifying g = -9.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. g = {5.141428429, -9.141428429}

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