Question

URGENT PLEASE Solve the equation using the quadratic formula. 3x^2 - 18 = -6

Answer 1

Answer: x = -2, x = 2

Explanation:

The quadratic formula:

`x=(-b+√(b^2-4ac) )/(2a) \\\\AND\\\\x = (-b-√(b^2-4ac) )/(2a) \\`

You can find the variables a, b, and c in the standard form of a quadratic equation:

`f(x)=ax^2 + bx+c`

Your equation:

`f(x)=3x^2 + 0x -12`

The variables are:

a = 3

b = 0

c = -12

Substitute those for the variables in the quadratic formula:

`x=(-0+√(0-(4*3*-12)))/(2(3)) \\\\AND\\\\x=(-0-√(0-(4*3*-12)))/(2(3)) \\`

You can simplify this to get:

`x=(-√(144))/(6) \\`

(or positive square root of 144.)

The square root of 144 is 12, and 12/6 = 2.

The x-values are -2 and 2.

Answer 2

x = 2 and x = -2

Explanation:

The quadratic formula of a quadratic of the form ax² + bx + c is:

x =
`(-b+√(b^2-4ac) )/(2a)` or x =
`(-b-√(b^2-4ac) )/(2a)`

Here, our equation is: 3x² - 18 = -6. Let's move all the terms to one side:

3x² - 12 = 0

a = 3 and c = -12. Notice that since there's no x term, b = 0.

Plug these into the quadratic formula:

x =
`(0+√(0^2-4*3*(-12)) )/(2*3)=(√(144) )/(6)=12/6=2`

or

x =
`(0-√(0^2-4*3*(-12)) )/(2*3)=(-√(144) )/(6)=-12/6=-2`

So, x = 2 and x = -2.