Respuesta :

wegnerkolmp2741o

Answer:

x = ±2 sqrt(3)

Step-by-step 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)

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[tex] \frac{3}{4} {x}^{2} - 4 = 5 \\ [/tex]

Add sides 4

[tex] \frac{3}{4} {x}^{2} - 4 + 4 = 5 + 4 \\ [/tex]

[tex] \frac{3}{4} {x}^{2} = 9 \\ [/tex]

Multiply sides by 4

[tex]4 \times \frac{3}{4} {x}^{2} = 4 \times 9 \\ [/tex]

[tex]3 {x}^{2} = 36[/tex]

Divide sides by 3

[tex] \frac{3 {x}^{2} }{3} = \frac{36}{3} \\ [/tex]

[tex] {x}^{2} = 12[/tex]

[tex]x = ± \: \sqrt{12} [/tex]

[tex]x = ± \: \sqrt{4 \times 3} [/tex]

[tex]x = ± \: \sqrt{ {2}^{2} \times 3 } [/tex]

[tex]x = ± \: 2 \sqrt{3} [/tex]

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