what is the positive solution of the equation x^2 = 2x + 35? solve by factoring.
To solve the equation x^2 = 2x + 35 by factoring, we need to rearrange the equation to bring all terms to one side, making it equal to zero:
x^2 - 2x - 35 = 0
Now, we need to factorize the quadratic expression on the left side of the equation. To do this, we will find two numbers that multiply to give -35 and add to give -2.
The factors of -35 are: (-1, 35), (1, -35), (-5, 7), and (5, -7)
Among these pairs, the pair (-5, 7) adds up to -2, which is what we want.
So, we can factor the quadratic expression as (x - 5)(x + 7) = 0.
Now, according to the Zero Product Property, if a product of factors is equal to zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x - 5 = 0 or x + 7 = 0
Solving the first equation:
x = 5
Solving the second equation:
x = -7
So, the positive solution of the equation x^2 = 2x + 35, obtained by factoring, is x = 5.
x^2-2x-35 = 0
Well, the factors of 35 are 5 and 7.
They differ by 2, so ...