Solve the quadratic equation 2x2+5x−3=02𝑥2+5𝑥−3=0 using the quadratic formula. Please show all your work with the Quad Formula to earn your points. You can upload a photo of your work if you prefer. (4 points)
To solve the quadratic equation 2x^2 + 5x - 3 = 0 using the quadratic formula, we first identify the values of a, b, and c in the general form of a quadratic equation ax^2 + bx + c = 0.
In this case:
a = 2
b = 5
c = -3
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values of a, b, and c, we get:
x = (-5 ± √(5^2 - 4*2*(-3))) / 2*2
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √49) / 4
x = (-5 ± 7) / 4
Now we find the two possible solutions by considering both the positive and negative square root:
1. x = (-5 + 7) / 4 = 2 / 4 = 0.5
2. x = (-5 - 7) / 4 = -12 / 4 = -3
Therefore, the solutions to the quadratic equation 2x^2 + 5x - 3 = 0 are x = 0.5 and x = -3.