The quadratic equation frequently appears in both the equilibrium and acid-base sections of General Chemistry. Therefore, it is useful to refresh the use of the quadratic before applying it to chemistry questions. Which of the following answers is a viable solution to the following equation:
2x2 + 8x + 3 = 0
just use the quadratic formula.
To find the solution to the quadratic equation 2x^2 + 8x + 3 = 0, you can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, the coefficients are:
a = 2
b = 8
c = 3
Substituting these values into the quadratic formula, we can solve for x:
x = (-8 ± √(8^2 - 4 * 2 * 3)) / (2 * 2)
x = (-8 ± √(64 - 24)) / 4
x = (-8 ± √40) / 4
Simplifying further:
x = (-8 ± 2√10) / 4
x = -2 ± √10 / 2
Therefore, the solutions to the quadratic equation 2x^2 + 8x + 3 = 0 are:
x = (-2 + √10)/2
x = (-2 - √10)/2
These are the two viable solutions to the equation.