Solve Using the Quadratic Formula 2x^2+5x+3=0

Problem

2*x2+5*x+3=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=5

c=3

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−5±√(,5−4*(2)*(3)))/(2*(2))

4. Simplify the expression inside the square root, known as the discriminant.

x=(−5±√(,25−24))/4

x=(−5±√(,1))/4

5. Evaluate the square root and split the expression into two possible solutions for x

x=(−5±1)/4

6. Calculate the first solution using the plus sign.

x=(−5+1)/4

x=(−4)/4

x=−1

7. Calculate the second solution using the minus sign.

x=(−5−1)/4

x=(−6)/4

x=−3/2

Final Answer

x=−1,−3/2

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