Solve Using the Quadratic Formula x^2-13x+42=0

Problem

x2−13*x+42=0

Solution

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

a=1

b=−13

c=42

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=(−(−13)±√(,(−13)2−4*(1)*(42)))/(2*(1))

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

x=(13±√(,169−168))/2

x=(13±√(,1))/2

5. Evaluate the square root.

x=(13±1)/2

6. Solve for both possible values of x

x=(13+1)/2=14/2=7

x=(13−1)/2=12/2=6

Final Answer

x=7,6

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