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. $5 + 6m^2 = 269$
5. $2(y^2 - 4) = 20$
6. $4x^2 - 3 = 2x^2 - 3$

Explanation:

Step1: Isolate $x^2$, take square roots

$x^2=17 \implies x=\pm\sqrt{17} \approx \pm4.1$

Step2: Isolate $n^2$, take square roots

$n^2+9=81 \implies n^2=72 \implies n=\pm\sqrt{72} \approx \pm8.5$

Step3: Isolate $x^2$, check validity

$-8x^2+9=777 \implies -8x^2=768 \implies x^2=-96$
No real solutions (square of real number cannot be negative)

Step4: Isolate $m^2$, take square roots

$5+6m^2=269 \implies 6m^2=264 \implies m^2=44 \implies m=\pm\sqrt{44} \approx \pm6.6$

Step5: Isolate $y^2$, take square roots

$2(y^2-4)=20 \implies y^2-4=10 \implies y^2=14 \implies y=\pm\sqrt{14} \approx \pm3.7$

Step6: Isolate $x^2$, solve for $x$

$4x^2-3=2x^2-3 \implies 2x^2=0 \implies x^2=0 \implies x=0$

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. $m \approx 6.6$ and $m \approx -6.6$
5. $y \approx 3.7$ and $y \approx -3.7$
6. $x=0$