Question

Solve the following quadratic equation using square roots: −9+(x−3)2−4/−4 .(1 point) Responses {28,−22} left brace 28 comma negative 22 right brace {2,−8} left brace 2 comma negative 8 right brace {16,−10} left brace 16 comma negative 10 right brace {8,−2}

Answer 1

To solve the quadratic equation, we need to simplify the expression first.

Start with the given expression: -9 + (x - 3)^2 - 4/-4

The expression -4/-4 simplifies to 1, so we have: -9 + (x - 3)^2 - 1

Next, we simplify the expression (x - 3)^2. The square of a binomial (x - 3)^2 can be expanded using the formula (a - b)^2 = a^2 - 2ab + b^2. In this case, a = x and b = 3.

(x - 3)^2 = x^2 - 2(x)(3) + 3^2
= x^2 - 6x + 9

Now substitute the simplified expression (x^2 - 6x + 9) back into the original equation:

-9 + (x^2 - 6x + 9) - 1

Combine like terms: -9 + 9 - 1 + x^2 - 6x

Simplifying further we have: x^2 - 6x - 1

This is our quadratic equation, and we can solve it by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 1, b = -6, and c = -1.

x = (-(-6) ± √((-6)^2 - 4(1)(-1))) / 2(1)
x = (6 ± √(36 + 4)) / 2
x = (6 ± √40) / 2
x = (6 ± 2√10) / 2
x = 3 ± √10

Therefore, the solutions to the quadratic equation are:
{x = 3 + √10, x = 3 - √10}