Question

you try: solve each equation. round to the nearest tenth if needed.

1. $x^2 = 17$
2. $n^2 + 9 = 81$
3. $-8x^2 + 9 = 777$
4. $5 + 6n^2 = 269$
5. $2(y^2 - 4) = 20$
6. $4x^2 - 3 = 2x^2 - 3$

Explanation:

5) Step1: Take square root of both sides

$x = \pm\sqrt{17}$

5) Step2: Calculate decimal value

$\sqrt{17} \approx 4.1$

6) Step1: Isolate $n^2$ term

$n^2 = 81 - 9 = 72$

6) Step2: Take square root of both sides

$n = \pm\sqrt{72} = \pm6\sqrt{2}$

6) Step3: Calculate decimal value

$6\sqrt{2} \approx 8.5$

7) Step1: Isolate $x^2$ term

$-8x^2 = 777 - 9 = 768$

7) Step2: Solve for $x^2$

$x^2 = \frac{768}{-8} = -96$

7) Step3: Analyze for real solutions

No real solutions (square of real number cannot be negative)

8) Step1: Isolate $n^2$ term

$6n^2 = 269 - 5 = 264$

8) Step2: Solve for $n^2$

$n^2 = \frac{264}{6} = 44$

8) Step3: Take square root of both sides

$n = \pm\sqrt{44} = \pm2\sqrt{11}$

8) Step4: Calculate decimal value

$2\sqrt{11} \approx 6.6$

9) Step1: Divide both sides by 2

$y^2 - 4 = \frac{20}{2} = 10$

9) Step2: Isolate $y^2$ term

$y^2 = 10 + 4 = 14$

9) Step3: Take square root of both sides

$y = \pm\sqrt{14}$

9) Step4: Calculate decimal value

$\sqrt{14} \approx 3.7$

10) Step1: Isolate $x^2$ terms

$4x^2 - 2x^2 = -3 + 3$

10) Step2: Simplify equation

$2x^2 = 0$

10) Step3: Solve for $x$

$x^2 = 0 \implies x = 0$

Answer:

1. $x \approx 4.1$ and $x \approx -4.1$
2. $n \approx 8.5$ and $n \approx -8.5$
3. No real solutions
4. $n \approx 6.6$ and $n \approx -6.6$
5. $y \approx 3.7$ and $y \approx -3.7$
6. $x = 0$