Solve Using the Quadratic Formula x^2-3x-40=0

Problem

x2−3*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=−3

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 values of a b and c into the formula.

x=(−(−3)±√(,(−3)2−4*(1)*(−40)))/(2*(1))

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

x=(3±√(,9+160))/2

x=(3±√(,169))/2

5. Evaluate the square root of 169

x=(3±13)/2

6. Solve for the two possible values of x by calculating both the addition and subtraction cases.

(x_1)=(3+13)/2=16/2=8

(x_2)=(3−13)/2=(−10)/2=−5

Final Answer

x=8,−5

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