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 standard form a*x2+b*x+c=0

a=1

b=−5

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=(−(−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±√(,1))/2

5. Evaluate the square root.

x=(5±1)/2

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

x=(5+1)/2=6/2=3

x=(5−1)/2=4/2=2

Final Answer

x=2,3

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