When a quadratic equation is solved by extracting its roots, the solution must contain the sign ±.
The solutions to the equations are:
- [tex]x = \±6[/tex].
- [tex]x = \±5[/tex].
- [tex]x = \±4[/tex]
[tex](1)\ x^2 = 36[/tex]
Take square roots of both sides
[tex]\sqrt{x^2} = \sqrt{36[/tex]
[tex]x = \sqrt{36[/tex]
The square roots of 36 are 6 and -6.
So, we have:
[tex]x = \±6[/tex]
[tex](2)\ x^2 - 16 = 9[/tex]
Add 16 to both sides
[tex]x^2 - 16 +16= 9 + 16[/tex]
[tex]x^2 = 25[/tex]
Take square roots of both sides
[tex]\sqrt{x^2} = \sqrt{25[/tex]
[tex]x = \sqrt{25[/tex]
The square roots of 25 are 5 and -5.
So, we have:
[tex]x = \±5[/tex]
[tex](3)\ 2x^2 - 32 = 0[/tex]
Add 32 to both sides
[tex]2x^2 - 32+32 = 0+32[/tex]
[tex]2x^2 = 32[/tex]
Divide both sides by 2
[tex]\frac{2x^2}{2} = \frac{32}{2}[/tex]
[tex]x^2 = 16[/tex]
Take square roots of both sides
[tex]\sqrt{x^2} = \sqrt{16}[/tex]
[tex]x = \sqrt{16}[/tex]
[tex]x = \±4[/tex]
Read more about quadratic equations at:
https://brainly.com/question/17177510
