Let's solve each quadratic equation step-by-step to find the correct solution sets:
1. Equation: [tex]\(2x^2 - 32 = 0\)[/tex]
- Add 32 to both sides to isolate the quadratic term:
[tex]\(2x^2 = 32\)[/tex]
- Divide both sides by 2:
[tex]\(x^2 = 16\)[/tex]
- Take the square root of both sides:
[tex]\(x = \pm 4\)[/tex]
- Solution set: [tex]\([-4, 4]\)[/tex]
2. Equation: [tex]\(4x^2 - 100 = 0\)[/tex]
- Add 100 to both sides to isolate the quadratic term:
[tex]\(4x^2 = 100\)[/tex]
- Divide both sides by 4:
[tex]\(x^2 = 25\)[/tex]
- Take the square root of both sides:
[tex]\(x = \pm 5\)[/tex]
- Solution set: [tex]\([-5, 5]\)[/tex]
3. Equation: [tex]\(x^2 - 55 = 9\)[/tex]
- Add 55 to both sides to combine constants:
[tex]\(x^2 = 64\)[/tex]
- Take the square root of both sides:
[tex]\(x = \pm 8\)[/tex]
- Solution set: [tex]\([-8, 8]\)[/tex]
4. Equation: [tex]\(x^2 - 140 = -19\)[/tex]
- Add 140 to both sides to combine constants:
[tex]\(x^2 = 121\)[/tex]
- Take the square root of both sides:
[tex]\(x = \pm 11\)[/tex]
- Solution set: [tex]\([-11, 11]\)[/tex]
5. Equation: [tex]\(2x^2 - 18 = 0\)[/tex]
- Add 18 to both sides to isolate the quadratic term:
[tex]\(2x^2 = 18\)[/tex]
- Divide both sides by 2:
[tex]\(x^2 = 9\)[/tex]
- Take the square root of both sides:
[tex]\(x = \pm 3\)[/tex]
- Solution set: [tex]\([-3, 3]\)[/tex]
Now we can match each quadratic equation with its corresponding solution set:
- [tex]\(2x^2 - 32 = 0\)[/tex]: [-4, 4]
- [tex]\(4x^2 - 100 = 0\)[/tex]: [-5, 5]
- [tex]\(x^2 - 55 = 9\)[/tex]: [-8, 8]
- [tex]\(x^2 - 140 = -19\)[/tex]: [-11, 11]
- [tex]\(2x^2 - 18 = 0\)[/tex]: [-3, 3]
