math

Find all values of x satisfying the given condition

1.y1=x2+4x−6​, y2=−x2+10x−5 y1- y2=0

solve the equation by factoring

2. x2=4x+21

3. 16x2+2x-3=0

4. 45-45x=(7x+4)(x-1)

Solve the quadratic equation by completing the square.

5. (x−5)2=64

6. x2−6x=-4

7. x2+6x+4=0

8. x2 -15x+36=0

9.7x2−7x−1=0

Solve the equation using the quadratic formula.

10. x2+8x+12=0

11. 9x2=4x+2

Solve the equation by the method of your choice.

12. 3x2−x=2

13. 3x2=72

14. (3x+1)(x+2)=−1

15 (3x−5)2=25

16. 1/x+1/x+4=1/2

17. Use the Pythagorean Theorem and the square root property to solve the following problem. Express your answer in simplified radical form. Then find a decimal approximation to the nearest tenth.

A rectangular park is 18 miles long and 9 miles wide. How long is a pedestrian route that runs diagonally across the​ park?

In simplified radical​ form, the pedestrian route is [] miles long.

18. The area of a rectangular wall of a barn is 105 square feet. Its length is 8 feet longer than the width. Find the length and width of the wall of the barn.

The width is feet.

19. A pool measuring 18 meters by 22 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 1440 square​ meters, what is the width of the​ path in meters?

20. A machine produces open boxes using square sheets of metal. The machine cuts​ equal-sized squares measuring 4 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 400 cubic​ inches, find the length and width of the open box.

The length and width of the open box are both [] inches.