Solve Using the Quadratic Formula x^2+6x-16=0

Problem

x2+6*x−16=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=6

c=−16

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=(−(6)±√(,(6)2−4*(1)*(−16)))/(2*(1))

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

x=(−6±√(,36+64))/2

x=(−6±√(,100))/2

5. Evaluate the square root.

x=(−6±10)/2

6. Solve for both possible values of x by splitting the plus-minus sign.

x=(−6+10)/2⇒x=4/2⇒x=2

x=(−6−10)/2⇒x=(−16)/2⇒x=−8

Final Answer

x=2,−8

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