Answer: Therefore, the solutions to the equation g^2 + 4g - 32 = 0 are g = 4 and g = -8.
Step-by-step explanation:
To solve the quadratic equation g^2 + 4g - 32 = 0 by factoring, we need to find two numbers that multiply to -32 and add up to 4.
The two numbers are 8 and -4 because 8 * (-4) = -32 and 8 + (-4) = 4.
Now we rewrite the equation as:
g^2 + 8g - 4g - 32 = 0
g(g + 8) - 4(g + 8) = 0
(g - 4)(g + 8) = 0
Now, set each factor to zero:
g - 4 = 0 or g + 8 = 0
Solving for g:
g = 4 or g = -8
Therefore, the solutions to the equation g^2 + 4g - 32 = 0 are g = 4 and g = -8.
