Solve Using the Quadratic Formula 2x^2+7x-4=0

Problem

2*x2+7*x−4=0

Solution

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

a=2

b=7

c=−4

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

x=(−7±√(,7−4*(2)*(−4)))/(2*(2))

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

x=(−7±√(,49+32))/4

x=(−7±√(,81))/4

4. Evaluate the square root.

x=(−7±9)/4

5. Solve for both possible values of x by splitting the plus and minus signs.

(x_1)=(−7+9)/4=2/4=1/2

(x_2)=(−7−9)/4=(−16)/4=−4

Final Answer

x=1/2,−4

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