Solve Using the Quadratic Formula x^2-13x+40=0

Problem

x2−13*x+40=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=−13

c=40

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 into the quadratic formula.

x=(−(−13)±√(,(−13)2−4*(1)*(40)))/(2*(1))

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

x=(13±√(,169−160))/2

x=(13±√(,9))/2

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

x=(13±3)/2

6. Calculate the first solution using the plus sign.

x=(13+3)/2=16/2=8

7. Calculate the second solution using the minus sign.

x=(13−3)/2=10/2=5

Final Answer

x=8,5

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