Apply the Quadratic Formula x^2-5x+4

Problem

x2−5*x+4=0

Solution

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

a=1

b=−5

c=4

2. Substitute these values into the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−5)±√(,(−5)2−4*(1)*(4)))/(2*(1))

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

x=(5±√(,25−16))/2

x=(5±√(,9))/2

4. Evaluate the square root and solve for both possible values of x

x=(5±3)/2

5. Calculate the first solution using the plus sign.

x=(5+3)/2

x=4

6. Calculate the second solution using the minus sign.

x=(5−3)/2

x=1

Final Answer

x=4,1

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