Question
Solve using the quadratic formula
4w^2+2w-3=0
Write your answers as integers proper or improper fractions in simplest form or decimals rounded to the nearest hundredth
4w^2+2w-3=0
Write your answers as integers proper or improper fractions in simplest form or decimals rounded to the nearest hundredth
Answers
GPT 3.5
To solve the quadratic equation 4w^2 + 2w - 3 = 0 using the quadratic formula, we first need to identify the coefficients of the quadratic equation:
a = 4
b = 2
c = -3
Now, we can plug these values into the quadratic formula: w = (-b ± √(b^2 - 4ac)) / 2a
After substituting the values in, we get:
w = (-2 ± √(2^2 - 4 * 4 * -3)) / 2 * 4
w = (-2 ± √(4 + 48)) / 8
w = (-2 ± √52) / 8
Now we can simplify the square root of 52 to get decimal approximation:
√52 ≈ 7.21
Therefore, w = (-2 ± 7.21) / 8
w = (7.21 - 2) / 8 or w = (-7.21 - 2) / 8
The two solutions are:
w = 0.6525 or w = -1.1525
a = 4
b = 2
c = -3
Now, we can plug these values into the quadratic formula: w = (-b ± √(b^2 - 4ac)) / 2a
After substituting the values in, we get:
w = (-2 ± √(2^2 - 4 * 4 * -3)) / 2 * 4
w = (-2 ± √(4 + 48)) / 8
w = (-2 ± √52) / 8
Now we can simplify the square root of 52 to get decimal approximation:
√52 ≈ 7.21
Therefore, w = (-2 ± 7.21) / 8
w = (7.21 - 2) / 8 or w = (-7.21 - 2) / 8
The two solutions are:
w = 0.6525 or w = -1.1525