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.
