First, add color(red)(18) to each side of the equation to isolate the x term while keeping the equation balanced:
32x^2 - 18 + color(red)(18) = 0 + color(red)(18)
32x^2 - 0 = 18
32x^2 = 18
Next, divide each side of the equation by color(red)(32) to isolate the x^2 term while keeping the equation balanced:
(32x^2)/color(red)(32) = 18/color(red)(32)
(color(red)(cancel(color(black)(32)))x^2)/cancel(color(red)(32)) = (2 xx 9)/color(red)(2 xx 16)
x^2 = (color(red)(cancel(color(black)(2))) xx 9)/color(red)(color(black)(cancel(color(red)(2))) xx 16)
x^2 = 9/16
Now, take the square root of each side of the equation to solve for x while keeping the equation balanced. Remember, taking the square root of a number produces a negative and positive result:
sqrt(x^2) = sqrt(9/16)
x = sqrt(9)/sqrt(16)
x = +-3/4