Question

3/4 x^2-4=5

Extracting the Square Roots​

Answer 1

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`(3)/(4) {x}^(2) - 4 = 5 \\`

Add sides 4

`(3)/(4) {x}^(2) - 4 + 4 = 5 + 4 \\`

`(3)/(4) {x}^(2) = 9 \\`

Multiply sides by 4

`4 * (3)/(4) {x}^(2) = 4 * 9 \\`

`3 {x}^(2) = 36`

Divide sides by 3

`\frac{3 {x}^(2) }{3} = (36)/(3) \\`

`{x}^(2) = 12`

`x = ± \: √(12)`

`x = ± \: √(4 * 3)`

`x = ± \: \sqrt{ {2}^(2) * 3 }`

`x = ± \: 2 √(3)`

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Answer 2

x = ±2 sqrt(3)

Explanation:

3/4 x^2-4=5

Add 4 to each side

3/4 x^2-4+4=5+4

3/4 x^2=9

Multiply each side by 4/3

4/3 * 3/4 x^2 = 9 * 4/3

x^2 = 12

Take the square root of each side

sqrt(x^2) = ±sqrt(12)

x = ±sqrt(4*3)

x = ± sqrt(4) sqrt(3)

x = ±2 sqrt(3)