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:

Problem 5:

Step1: Take square roots

$\sqrt{x^2} = \pm\sqrt{17}$

Step2: Calculate & round

$x \approx \pm4.1$

Problem 6:

Step1: Isolate $n^2$

$n^2 = 81 - 9 = 72$

Step2: Take square roots & round

$\sqrt{n^2} = \pm\sqrt{72}$, $n \approx \pm8.5$

Problem 7:

Step1: Isolate $-8x^2$

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

Step2: Isolate $x^2$

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

Step3: Analyze square of real number

No real solution (square can't be negative)

Problem 8:

Step1: Isolate $6n^2$

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

Step2: Isolate $n^2$

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

Step3: Take square roots & round

$\sqrt{n^2} = \pm\sqrt{44}$, $n \approx \pm6.6$

Problem 9:

Step1: Isolate $(y^2-4)$

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

Step2: Isolate $y^2$

$y^2 = 10 + 4 = 14$

Step3: Take square roots & round

$\sqrt{y^2} = \pm\sqrt{14}$, $y \approx \pm3.7$

Problem 10:

Step1: Isolate $x^2$ terms

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

Step2: Simplify equation

$2x^2 = 0$

Step3: Solve for $x$

$x^2 = 0$, $x = 0$

Answer:

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