Solve the equation by factoring, show all work.
5x^2=80
5x^2 = 80.
5x^2-80 = 0,
5(x^2-16) = 0,
5(x-4)(x+4) = 0,
Divide both sides by 5:
(x+4)(x-4) = 0,
x+4 = 0, X = -4.
x-4 = 0, X = 4.
To solve the equation 5x^2 = 80 by factoring, we follow these steps:
Step 1: Set the equation equal to zero by subtracting 80 from both sides:
5x^2 - 80 = 0
Step 2: Factor out the greatest common factor (GCF), which is 5:
5(x^2 - 16) = 0
Step 3: Factor the quadratic expression inside the parentheses. To do this, we look for a pair of numbers whose product is -16 and whose sum is zero. In this case, the numbers are 4 and -4:
5(x + 4)(x - 4) = 0
Step 4: Apply the zero product property, which states that if a product of factors equals zero, then at least one of the factors must be zero. In this case, either (x + 4) = 0 or (x - 4) = 0.
For the first factor:
x + 4 = 0
Subtract 4 from both sides:
x = -4
For the second factor:
x - 4 = 0
Add 4 to both sides:
x = 4
So the solutions to the equation 5x^2 = 80 are x = -4 and x = 4.