Watch this video to go over how to solve a quadratic by factoring.%0D%0A%0D%0AThen solve the equation: x2−2x − 35 = 0 %0D%0A%0D%0A2%0D%0A−%0D%0A2%0D%0A%0D%0A %0D%0A−%0D%0A %0D%0A35%0D%0A %0D%0A=%0D%0A %0D%0A0%0D%0A %0D%0A for x.%0D%0A%0D%0APlease show all of your work.
To solve the equation x^2 - 2x - 35 = 0, we can use the method of factoring.
First, let's rearrange the equation to have the constant term on the right side:
x^2 - 2x = 35
Now, we need to factor the left side of the equation. We are looking for two numbers whose product is -35 (-1 * 35, 1 * -35, -5 * 7, 5 * -7) and whose sum is -2. The numbers that satisfy this condition are -7 and 5:
(x - 7)(x + 5) = 0
Now, we can apply the zero product property, which states that if a product of factors equals zero, then at least one of the factors must be equal to zero. In this case, we have two factors, so we set each factor equal to zero and solve for x:
x - 7 = 0
x = 7
x + 5 = 0
x = -5
Therefore, the solutions to the equation x^2 - 2x - 35 = 0 are x = 7 and x = -5.