Question

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

Answer 1

Answer:

37) ±√29 - 4

Completing the square utilizes this formula $(\frac{b}{2})^{2}$. We know that b=8, 8 can be plugged into this formula to get $(\frac{8}{2})^2$. 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 $(\frac{4}{2} )^2$. 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 :)