The steps Patel could use to solve the quadratic equation 8x^2 + 16x + 3 = 0 are:
1. Rewrite the equation in standard form: 8x^2 + 16x + 3 = 0
2. Use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where a = 8, b = 16, and c = 3.
3. Simplify the expression under the square root: √(16^2 - 4(8)(3)) = √(256 - 96) = √160 = 4√10
4. Substitute the values into the quadratic formula: x = (-16 ± 4√10) / 16
5. Simplify the expression: x = (-1 ± √10 / 2)
Therefore, the options that describe these steps are:
- Use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where a = 8, b = 16, and c = 3.
- Simplify the expression under the square root: √(16^2 - 4(8)(3)) = √(256 - 96) = √160 = 4√10
- Substitute the values into the quadratic formula: x = (-16 ± 4√10) / 16
So, the correct options are:
- Use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where a = 8, b = 16, and c = 3.
- Simplify the expression under the square root: √(16^2 - 4(8)(3)) = √(256 - 96) = √160 = 4√10
- Substitute the values into the quadratic formula: x = (-16 ± 4√10) / 16