Solve Using the Quadratic Formula r^2+3r-10=0

Problem

r2+3*r−10=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*r2+b*r+c=0

a=1

b=3

c=−10

2. State the quadratic formula for the variable r

r=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

r=(−(3)±√(,3−4*(1)*(−10)))/(2*(1))

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

r=(−3±√(,9+40))/2

r=(−3±√(,49))/2

5. Evaluate the square root.

r=(−3±7)/2

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

(r_1)=(−3+7)/2=4/2=2

(r_2)=(−3−7)/2=(−10)/2=−5

Final Answer

r=2,−5

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