Solve this quadratic equation. Be sure to give $$ 4 x^{2}-5=31 $$

Question

UpStudy AI · Accepted Answer

To solve the quadratic equation:

$$
4x^{2} - 5 = 31
$$

follow these steps:

1. **Isolate the quadratic term.**

Add 5 to both sides of the equation to move the constant term to the right side:

$$
   4x^{2} = 31 + 5
   $$
   
   $$
   4x^{2} = 36
   $$

2. **Solve for $$ x^{2} $$.**

Divide both sides by 4 to isolate $$ x^{2} $$:

$$
   x^{2} = \frac{36}{4}
   $$
   
   $$
   x^{2} = 9
   $$

3. **Take the square root of both sides.**

Remember that taking the square root yields both positive and negative solutions:

$$
   x = \pm\sqrt{9}
   $$
   
   $$
   x = \pm 3
   $$

4. **Write the final solutions.**

$$
   x = 3 \quad \text{and} \quad x = -3
   $$

**Therefore, the solutions to the equation $$ 4x^{2} - 5 = 31 $$ are $$ x = 3 $$ and $$ x = -3 $$.**
The solutions are $$ x = 3 $$ and $$ x = -3 $$.

Solve this quadratic equation. Be sure to give