Question

Solve each equation by completing the square. Write both answers separately.

Answer 1

37) ±√29 - 4

Completing the square utilizes this formula
`((b)/(2))^(2)`. We know that b=8, 8 can be plugged into this formula to get
`((8)/(2))^2`. Simplify to get 16. Now, we can add this into the equation to get
`k^(2)+8k+13=26`. Subtract 26 to both sides, so the equation can equal to 0.
`k^(2) +8k-13=0` would be the resulting equation. Now, let's use quadratic formula to find the solution. The quadratic formula is (-b+-√b^2-4ac) / 2a. Plug in all of our values to get (-8+-√8^2-4(1)(-13)/2(1). Simplify the equation to get ±√29 - 4.

38) ±√21 - 2

Let's use the same formula. b=4, so
`((4)/(2) )^2`. Simplify to get 4. Add that into the equation to get
`x^(2)+4x-5=12`. Subtract 8 on both sides, so the equation can equal to 0.
`x^(2)+4x-17=0` would be the result. Use the quadratic formula again to find the solution. Plug in all of the values to get ±√21 - 2

If you're confused on any part of the explanation, feel free to ask :)