solve by factoring x^2 -7x-72=0
So close!
x^2 - 6x - 72 = (x-12)(x+6)
x^2 - x - 72 = (x-9)(x+8)
no way
thanks for your help Damon!
sqrt (b^2-4ac) = sqrt (337)
that is not a perfect square so factoring will not work.
To solve the quadratic equation x^2 - 7x - 72 = 0 by factoring, we can follow these steps:
Step 1: Write down the equation: x^2 - 7x - 72 = 0.
Step 2: Find two numbers whose product is equal to the product of the coefficient of x^2 (which is 1) and the constant term (which is -72), and whose sum is equal to the coefficient of x (which is -7).
The two numbers that satisfy these conditions are 9 and -8.
Step 3: Rewrite the middle term (-7x) of the quadratic equation as the sum of the two numbers found in step 2:
x^2 + 9x - 8x - 72 = 0.
Step 4: Group the terms and factor out common factors:
(x^2 + 9x) + (-8x - 72) = 0.
Step 5: Factor out the greatest common factor from each group:
x(x + 9) - 8(x + 9) = 0.
Step 6: Factor out the common binomial factor (x + 9):
(x + 9)(x - 8) = 0.
Now, we can use the zero product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero.
Setting each factor equal to zero gives us the following two equations:
x + 9 = 0 and x - 8 = 0.
Solving these equations, we find:
x = -9 and x = 8.
Therefore, the solutions to the quadratic equation x^2 - 7x - 72 = 0 are x = -9 and x = 8.