Solve Using the Quadratic Formula x^2-5x-6=0

Problem

x2−5*x−6=0

Solution

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

a=1

b=−5

c=−6

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

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−(−5)±√(,(−5)2−4*(1)*(−6)))/(2*(1))

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

x=(5±√(,25+24))/2

x=(5±√(,49))/2

5. Evaluate the square root and split the equation into two possible cases for x

x=(5±7)/2

6. Calculate the first solution by using the addition case.

x=(5+7)/2

x=12/2

x=6

7. Calculate the second solution by using the subtraction case.

x=(5−7)/2

x=(−2)/2

x=−1

Final Answer

x=6,−1

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