Question

Solve for x. Write the smaller solution first, and the larger solution second.
5x^2 + 45x + 90 = 05x
2
+45x+90=0

Answer 1

Answer:

Step-by-step explanation:

(5x2 - 45x) + 90 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

5x2 - 45x + 90 = 5 • (x2 - 9x + 18)

Trying to factor by splitting the middle term

3.2 Factoring x2 - 9x + 18

The first term is, x2 its coefficient is 1 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is +18

Step-1 : Multiply the coefficient of the first term by the constant 1 • 18 = 18

Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is -9 .

-18 + -1 = -19

-9 + -2 = -11

-6 + -3 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -3

x2 - 6x - 3x - 18

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-6)

Add up the last 2 terms, pulling out common factors :

3 • (x-6)

Step-5 : Add up the four terms of step 4 :

(x-3) • (x-6)

Which is the desired factorization

Equation at the end of step 3 :

5 • (x - 3) • (x - 6) = 0

Answer 2

Answer:

x=0 satisfying both sides. Hence x=0