Solve Using the Quadratic Formula m^2-5m-14=0

Problem

m2−5*m−14=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*m2+b*m+c=0

a=1

b=−5

c=−14

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

m=(−b±√(,b2−4*a*c))/(2*a)

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

m=(−(−5)±√(,(−5)2−4*(1)*(−14)))/(2*(1))

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

m=(5±√(,25+56))/2

m=(5±√(,81))/2

5. Evaluate the square root and solve for the two possible values of m

m=(5±9)/2

6. Calculate the first solution using the addition case.

m=(5+9)/2=14/2=7

7. Calculate the second solution using the subtraction case.

m=(5−9)/2=(−4)/2=−2

Final Answer

m=7,−2

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