Question

Solve each equation by factoring. Show work.

5n^2+45n+90=0
a. n = -6, n = -3
b. n = -5, n = -9
c. n = 3, n = -6
d. n = -3, n = -6

Answer 1

(d) n = - 3, n = - 6

Step-by-step explanation:

given the quadratic equation

5n² + 45n + 90 = 0 ( divide through by 5 )

n² + 9n + 18 = 0

to factorise

consider the factors of the constant term (+ 18) which sum to give the coefficient of the n- term (+ 9)

the factors are + 3 and + 6 , since

+ 3 × + 6 = + 18 and + 3 + 6 = + 9

use these factors to split the n- term

n² + 3n + 6n + 18 = 0 ( factor the first/second and third/fourth terms )

n(n + 3) + 6(n + 3) = 0 ← factor out (n + 3) from each term

(n + 3)(n + 6) = 0 ← in factored form

equate each factor to zero and solve for n

n + 3 = 0 ( subtract 3 from both sides )

n = - 3

n + 6 = 0 ( subtract 6 from both sides )

n = - 6

the solutions are n = - 3 , n = - 6

Answer 2

To solve the equation 5n^2+45n+90=0 by factoring, divide the equation by 5 and factor the quadratic expression. The correct answer is d. n = -3, n = -6.

Step-by-step explanation:

To solve the equation 5n^2+45n+90=0 by factoring, we can first divide the entire equation by 5 to simplify it: n^2 + 9n + 18 = 0. Next, we need to factor in the quadratic expression. The factors of 18 that add up to 9 are 3 and 6. Therefore, the factored equation is (n+3)(n+6) = 0. To find the values of n, we set each factor equal to zero: n+3 = 0 or n+6 = 0. Solving for n gives us n = -3 or n = -6. Therefore, the correct answer is d. n = -3, n = -6.