Solve for g: 26g^2 + 17g = 0

Understand the Problem

The question asks us to solve for (g) in the equation (26g^2 + 17g = 0). This is a quadratic equation that can be solved by factoring out a common term, in this case (g).

Answer

$g = 0, -\frac{17}{26}$

Steps to Solve

Factor out the common term (g)

Both terms in the equation (26g^2 + 17g = 0) have (g) as a factor. Factoring out (g) from the equation, we get:

$$g(26g + 17) = 0$$

Set each factor equal to zero

Now, we set each factor equal to zero and solve for (g):

$$g = 0$$

and

$$26g + 17 = 0$$

Solve for (g) in the second equation

Subtract 17 from both sides:

$$26g = -17$$

Divide both sides by 26:

$$g = -\frac{17}{26}$$

Identify both solutions for g

The solutions are (g = 0) and (g = -\frac{17}{26}).

$g = 0, -\frac{17}{26}$

More Information

The quadratic equation has two solutions when solved. Factoring is a useful approach when the equation can be easily factored.

Tips

A common mistake is to divide both sides of the original equation (26g^2 + 17g = 0) by (g). This would give you (26g + 17 = 0), leading to the solution (g = -\frac{17}{26}), but you would miss the solution (g = 0). Factoring is the correct approach to find all solutions.

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