Watch this video to go over how to solve a quadratic by factoring. Then solve the equation: x2−2x − 35 = 0 for x. Please show all of your work.
Unfortunately, as a text-based AI, I am unable to watch videos. However, I can help you solve the quadratic equation x^2 - 2x - 35 = 0 by factoring.
To solve a quadratic equation by factoring, we need to find two numbers (let's call them a and b) whose product is equal to the product of the coefficient of x^2 (which is 1 in this case) and the constant term (which is -35), and simultaneously satisfies the equation: a + b = coefficient of x term (which is -2 in this case).
In our equation x^2 - 2x - 35 = 0, we can see that -7 and 5 are two such numbers.
So, we can rewrite the equation as follows by splitting the middle term (-2x) using these numbers:
x^2 - 7x + 5x - 35 = 0
Next, we group the terms and factor them:
x(x - 7) + 5(x - 7) = 0
We see that we have a common factor of (x - 7), so we can factor it out:
(x - 7)(x + 5) = 0
Now, to find the values of x, we set each factor equal to zero and solve for x:
x - 7 = 0 or x + 5 = 0
Solving these two equations, we get:
x = 7 or x = -5
So, the solutions to the quadratic equation x^2 - 2x - 35 = 0 are x = 7 and x = -5.