Question

Solve the quadratic equation x²−12x+27=0 by factoring. Choose the correct solution from the following options:

A. x=3, x=9
B. x=3, x=−9
C. x=−3, x=9
D. x=−3, x=−9

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$\sf x^2 - 12x + 27 = 0$}`

`\Large \text{$\sf x^2 - 9x - 3x + 27 = 0$}`

`\Large \text{$\sf x\:.\:(x - 9) - 3\:.\:(x - 9) = 0$}`

`\Large \text{$\sf (x - 9)\:.\:(x - 3) = 0$}`

`\Large \text{$\sf x - 9 = 0 \rightarrow x = 9$}`

`\Large \text{$\sf x - 3 = 0 \rightarrow x = 3$}`

`\Large \boxed{\boxed{\text{$\sf S = \{3,\:9\}$}}}`

Answer 2

The quadratic equation x²−12x+27=0 is factored as (x−3)(x−9)=0, resulting in the solutions x=3 and x=9, which corresponds to option A.

Step-by-step explanation:

To solve the quadratic equation x²−12x+27=0 by factoring, we seek two numbers that multiply to give the constant term (27) and also add to give the coefficient of the x term (−12). The numbers that satisfy these conditions are −9 and −3, because (−9)(−3) = 27 and (−9) + (−3) = −12. Therefore, we can express the quadratic equation as (x−3)(x−9) = 0.

This implies that either x−3 = 0 or x−9 = 0, giving us the solutions x = 3 and x = 9 respectively.

So the correct solution from the provided options is: A. x = 3, x = 9.