Completing the square and the quadratic formula

Answer: x=4+√6x=4−√6

1. Move the constant: x2−8x=−10.
2. Add 16 to both sides to complete the square: (x−4)2=6.
3. Take both square roots: x−4=±√6.
4. Therefore x=4+√6 or x=4−√6.
5. Enter both roots, in either order.

Answer: x=−4+√7x=−4−√7

1. Move the constant: x2+8x=−9.
2. Add 16 to both sides to complete the square: (x+4)2=7.
3. Take both square roots: x+4=±√7.
4. Therefore x=−4+√7 or x=−4−√7.
5. Enter both roots, in either order.

Answer: x=27+√21​x=27−√21​

1. Write x2−7x=−7.
2. Half the x coefficient is 2−7​;
3. its square is 449​.
4. Add 449​ to both sides: (x−27​)2=421​.
5. Take both square roots
6. subtract 2−7​:x=27±√21​.
7. Therefore x=27+√21​ or x=27−√21​.
8. Enter both roots, in either order.