Answer:
-6, 1
Explanation:
You want the real roots of the quadratic x^2 + 5x = 6.
Factorization
The roots are easily identified from the factored form of the equation. The factors will involve the constants that have a sum of +5 and a product of -6.
-6 = 6·(-1) = 3·(-2)
Sums of the factor pairs are 5 and 1. We will use the constants that have a sum of 5.
x^2 +5x = 6 . . . . . . given
x^2 +5x -6 = 0 . . . . . standard form
(x +6)(x -1) = 0 . . . . . . . factored form
Zero product rule
The zero product rule tells us that a product will be zero if and only if at least one of the factors is zero. To find the values of x, we set the factors equal to zero and solve for x.
(x +6) = 0 ⇒ x = -6
(x -1) = 0 ⇒ x = 1
x = -6, or x = 1 . . . . . . . . roots of the quadratic