Solve Using the Quadratic Formula 2x^2-4x-3=0

Problem

2*x2−4*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=2

b=−4

c=−3

2. State the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

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

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

x=(4±√(,16+24))/4

x=(4±√(,40))/4

5. Simplify the radical by factoring out the largest perfect square.

x=(4±√(,4⋅10))/4

x=(4±2√(,10))/4

6. Divide both terms in the numerator by the denominator to find the final simplified values.

x=(2±√(,10))/2

Final Answer

x=(2±√(,10))/2

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