Solve 2x(squared)-3x-2=0 using the quadratic formula. Can someone explain this to me please?
match
2x^2 - 3x - 2 = 0 with
ax^2 + bx + c = 0
so a=2, b=-3, c=-2
the formula says
x = (-b ±√(b^2 - 4ac))/(2a)
substitute the above values and simplify
(did you get x=2, x=-1/2 ?)
Of course! To solve the quadratic equation 2x^2 - 3x - 2 = 0 using the quadratic formula, we follow a step-by-step process.
Step 1: Identify the coefficients
The quadratic equation is in the form ax^2 + bx + c = 0, so we need to identify the values of a, b, and c. In this case, a = 2, b = -3, and c = -2.
Step 2: Apply the quadratic formula
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). We can now substitute the values of a, b, and c into this formula.
x = (-(-3) ± √((-3)^2 - 4(2)(-2))) / (2(2))
Simplifying it further:
x = (3 ± √(9 + 16)) / 4
x = (3 ± √25) / 4
Step 3: Simplify the square root
√25 equals 5, so we can simplify our equation:
x = (3 ± 5) / 4
This gives us two possible solutions:
x1 = (3 + 5) / 4 = 8 / 4 = 2
x2 = (3 - 5) / 4 = -2 / 4 = -0.5
Therefore, the solutions to the quadratic equation 2x^2 - 3x - 2 = 0 are x1 = 2 and x2 = -0.5.