Solve Using the Quadratic Formula 2x^2-x-6=0

Problem

2*x2−x−6=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=−1

c=−6

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=(−(−1)±√(,(−1)2−4*(2)*(−6)))/(2*(2))

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

x=(1±√(,1+48))/4

x=(1±√(,49))/4

5. Evaluate the square root.

x=(1±7)/4

6. Solve for the two possible values of x by calculating both the addition and subtraction cases.

x=(1+7)/4=8/4=2

x=(1−7)/4=(−6)/4=−3/2

Final Answer

x=2,−3/2

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