Solve Using the Quadratic Formula 4k(k+6)=6

Problem

4*k*(k+6)=6

Solution

1. Distribute the 4*k into the parentheses to expand the left side of the equation.

4*k2+24*k=6

2. Rearrange the equation into standard quadratic form a*k2+b*k+c=0 by subtracting 6 from both sides.

4*k2+24*k−6=0

3. Simplify the equation by dividing all terms by the greatest common factor, which is 2

2*k2+12*k−3=0

4. Identify the coefficients for the quadratic formula k=(−b±√(,b2−4*a*c))/(2*a)

a=2

b=12

c=−3

5. Substitute the values into the quadratic formula.

k=(−12±√(,12−4*(2)*(−3)))/(2*(2))

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

k=(−12±√(,144+24))/4

k=(−12±√(,168))/4

7. Simplify the radical √(,168) by factoring out the largest perfect square, which is 4

√(,168)=√(,4⋅42)=2√(,42)

k=(−12±2√(,42))/4

8. Reduce the fraction by dividing the numerator and denominator by 2

k=(−6±√(,42))/2

Final Answer

k=(−6±√(,42))/2

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