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.
