How do you solve #3x^2-12=0# using the quadratic formula?

1 Answer
Aug 20, 2017

Answer:

See a solution process below:

Explanation:

First, we can divide each side of the equation by #color(red)(3)# to reduce the coefficients while keeping the equation balanced:

#(3x^2 - 12)/color(red)(3) = 0/color(red)(3)#

#(3x^2)/color(red)(3) - 12/color(red)(3) = 0#

#x^2 - 4 = 0#

We can rewrite this expression as:

#x^2 + 0x - 4 = 0#

We can now use the quadratic equation to solve this problem:

The quadratic formula states:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#

Substituting:

#color(red)(1)# for #color(red)(a)#

#color(blue)(0)# for #color(blue)(b)#

#color(green)(-4)# for #color(green)(c)# gives:

#x = (-color(blue)(0) +- sqrt(color(blue)(0)^2 - (4 * color(red)(1) * color(green)(-4))))/(2 * color(red)(1))#

#x = (+- sqrt(0 - (-16)))/2#

#x = (+- sqrt(0 + 16))/2#

#x = (+- sqrt(16))/2#

#x = (+-4)/2#

#x = +-2#

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Another way to solve this problem without using the quadratic formula is to add #color(red)(12)# to each side of the equation to isolate the #x^2# term:

#3x^2 - 12 + color(red)(12) = 0 + color(red)(12)#

#3x^2 - 0 = 12#

#3x^2 = 12#

Next, divide each side of the equation by #color(red)(3)# to isolate the #x^2# while keeping the equation balanced:

#(3x^2)/color(red)(3) = 12/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x^2)/cancel(color(red)(3)) = 4#

#x^2 = 4#

Now, take the square root of each side of the equation to solve for #x# while keeping the equation balanced. Remember the square root of a number produces a positive AND negative result:

#sqrt(x^2) = +-sqrt(4)#

#x = +-2#

The same result as above.