How do you solve 32x^2-18=0?

3 Answers
Apr 26, 2017

See the solution process below:

Explanation:

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

Apr 26, 2017

x = 0.75

Explanation:

32x^2-18=0
32x^2-18+18=0+18
32x^2=18
32x^2/32=18/32
x^2=0.5625
sqrt(x^2)=sqrt(0.5625)
x=0.75

Apr 26, 2017

color(blue)(x=3/4 or color(blue)(x=-3/4

Explanation:

32x^2-18=0

Take out the common factor first

:.2(16x^2-9)=0

:.2(4^2x^2-3^2)=0

Divide both sides by 2

:.(4^2x^2-3^2)=0

:.(4x-3)(4x+3)=0

:.4x-3=0,4x+3=0

:.4x=3,4x=-3

:.color(blue)(x=3/4,x=-3/4

substitute color(blue)(x=3/4=0.75

:.32(color(blue)0.75)^2-18=0

:.32(0.5625)-18=0

18-18=0

substitute x=-3/4=-0.75

:.32(color(blue)-0.75)^2-18=0

:.32(0.5625)-18=0

:.18-18=0