Quiz On Completing The Square

The given quadratic expression can be factored into (x-4)^2. This is because the expression follows the pattern of a perfect square trinomial, where the first term is the square of the binomial's first term (x^2), the last term is the square of the binomial's second term (16), and the middle term is twice the product of the binomial's terms (-8x). Therefore, the correct factored form is (x-4)^2.

Adding +9 to x^2+6x would make it a perfect square trinomial because if we factor x^2+6x+9, it can be written as (x+3)(x+3), which is the square of (x+3). Therefore, +9 is the correct term to make x^2+6x a perfect square trinomial.

To complete the square for the given equation, x^2-8x = 10, we need to take half of the coefficient of x (which is 8) and square it. Taking half of 8 gives us 4, and squaring it gives us 16. Thus, we need to add 16 to both sides of the equation to complete the square.

Completing the square is a method used to rewrite a quadratic expression in the form of a perfect square trinomial. By adding and subtracting a constant term to the quadratic expression, we can create a perfect square trinomial with a square term and a constant term. This allows us to easily factorize the quadratic expression and solve for its roots. Therefore, the goal of completing the square is to transform the quadratic expression into a perfect square trinomial.

To complete the square on the given quadratic equation, the first step is to divide the entire equation by the coefficient of x^2, which is 4. This step is necessary to make the coefficient of x^2 equal to 1, which allows for easier completion of the square.