Question

x2 + 30x + 216 solve by splitting the middle term ​

Answer 1

x2 +12x+18(x+12)

x(x+12) +18(x+12)

(x+12) (x+18)

Answer 2

The solutions to the quadratic equation $x^2 + 30x + 216$ are:

x = -12 and x = -18.

To solve this quadratic equation by splitting the middle term, we need to find two numbers whose product is equal to the product of the first and last coefficients, and whose sum is equal to the middle term's coefficient.

The first coefficient is 1, the middle coefficient is 30, and the last coefficient is 216. We need to find two numbers whose product is 1 x 216 = 216, and whose sum is 30.

One way to do this is to factor 216 into its prime factors: 2 x 2 x 2 x 3 x 3 x 3. Then we can pair these factors to get two numbers whose product is 216: (2 x 2 x 3) and (2 x 3 x 3). Their sum is 2 + 2 + 3 + 3 + 3 = 13.

Hence, the middle term can be divided as follows:

$x^2 + 30x + 216 = x^2 + 12x + 18x + 216$

= x(x + 12) + 18(x + 12)

= (x + 12)(x + 18)

Therefore, the solutions to the quadratic equation $x^2 + 30x + 216$ are:

x = -12 and x = -18.

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