Question

b. $x=4,-4$
c. $x=8,-8$
d. $x=1.2,-1.2$
e. $x=5,-5$

1. $2x^{2}-3=29$
2. $-1-5x^{2}=-321$
3. $3x^{2}=75$
4. $8x^{2}+9=313$
5. $32=25x^{2}-4$

Explanation:

Step1: Isolate $x^2$ term (Q1)

Add 3 to both sides:
$2x^2 = 29 + 3$
$2x^2 = 32$
Divide by 2:
$x^2 = \frac{32}{2} = 16$
Take square root:
$x = \pm\sqrt{16} = \pm4$

Step2: Isolate $x^2$ term (Q2)

Add 1 to both sides:
$-5x^2 = -321 + 1$
$-5x^2 = -320$
Divide by -5:
$x^2 = \frac{-320}{-5} = 64$
Take square root:
$x = \pm\sqrt{64} = \pm8$

Step3: Isolate $x^2$ term (Q3)

Divide by 3:
$x^2 = \frac{75}{3} = 25$
Take square root:
$x = \pm\sqrt{25} = \pm5$

Step4: Isolate $x^2$ term (Q4)

Subtract 9 from both sides:
$8x^2 = 313 - 9$
$8x^2 = 304$
Divide by 8:
$x^2 = \frac{304}{8} = 38$
Take square root:
$x = \pm\sqrt{38} \approx \pm6.16$ (not in given options)

Step5: Isolate $x^2$ term (Q5)

Add 4 to both sides:
$25x^2 = 32 + 4$
$25x^2 = 36$
Divide by 25:
$x^2 = \frac{36}{25}$
Take square root:
$x = \pm\sqrt{\frac{36}{25}} = \pm\frac{6}{5} = \pm1.2$

Answer:

1. $x=4,-4$ (matches option b)
2. $x=8,-8$ (matches option c)
3. $x=5,-5$ (matches option e)
4. $x=\pm\sqrt{38}\approx\pm6.16$
5. $x=1.2,-1.2$ (matches option d)