Solve Using the Quadratic Formula 4k(k+13)=13

Problem

4*k*(k+13)=13

Solution

1. Distribute the 4*k on the left side of the equation to remove the parentheses.

4*k2+52*k=13

2. Rearrange the equation into standard quadratic form a*k2+b*k+c=0 by subtracting 13 from both sides.

4*k2+52*k−13=0

3. Identify the coefficients a b and c for use in the quadratic formula.

a=4

b=52

c=−13

4. Apply the quadratic formula k=(−b±√(,b2−4*a*c))/(2*a) by substituting the identified values.

k=(−52±√(,52−4*(4)*(−13)))/(2*(4))

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

k=(−52±√(,2704+208))/8

k=(−52±√(,2912))/8

6. Simplify the radical by finding the largest perfect square factor of 2912 which is 64×45.5 (or more precisely, 256×11.375. Let's use 2912=16×182 or 64×45.5 Actually, 2912=16×11.375 is not right. 2912=64×45.5 Let's try 2912=16×183 no. 2912=64×45.5 Let's try 16×182 182=2×91=2×7×13 So 2912=16×2×91=32×91 Wait, 2912=16×182=16×2×91=32×7×13 The largest square factor is 16

k=(−52±4√(,182))/8

7. Reduce the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4

k=(−13±√(,182))/2

Final Answer

k=(−13±√(,182))/2

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