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

Extracting the Square Roots​

2 Answers

4 votes

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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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3 votes

Answer:

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)

User Virne
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