Solve Using the Quadratic Formula 8x^2-2x-3=0

Problem

8*x2−2*x−3=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*x2+b*x+c=0

a=8

b=−2

c=−3

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−2)±√(,(−2)2−4*(8)*(−3)))/(2*(8))

3. Simplify the expression inside the square root (the discriminant).

x=(2±√(,4+96))/16

x=(2±√(,100))/16

4. Evaluate the square root and solve for the two possible values of x

x=(2±10)/16

5. Calculate the first solution by using the plus sign.

x=(2+10)/16

x=12/16

x=3/4

6. Calculate the second solution by using the minus sign.

x=(2−10)/16

x=(−8)/16

x=−1/2

Final Answer

x=3/4,−1/2

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