For this case we must solve each of the equations proposed:
A) [tex]m ^ 2 + 9 = 58[/tex]
Subtracting 9 from both sides of the equation we have:
[tex]m ^ 2 = 49[/tex]
Applying root to both sides of the equation:
[tex]m = \sqrt {49}\\m = \pm7[/tex]
B) [tex]7e ^ 2 = 28[/tex]
We divide between 7 on both sides of the equation:
[tex]e ^ 2 = \frac {28} {7}\\e ^ 2 = 4[/tex]
We apply root to both sides of the equation:
[tex]e = \pm \sqrt {4}\\e = \pm2[/tex]
C) [tex]d ^ 2 + 6 = 70[/tex]
Subtracting 6 on both sides of the equation:
[tex]d ^ 2 = 64[/tex]
We apply root to both sides of the equation:
[tex]d =\pm \sqrt {64}\\d = \pm8[/tex]
D) [tex]\frac {1} {2} n ^ 2-10 = 62[/tex]
We add 10 to both sides of the equation:
[tex]\frac {1} {2} n ^ 2 = 72[/tex]
We multiply by 2 both sides of the equation:
[tex]n ^ 2 = 144[/tex]
We apply root to both sides of the equation:
[tex]n = \pm \sqrt {144}\\n =\pm12[/tex]
Answer:
[tex]m = \pm7\\e = \pm2\\d = \pm8\\n = \pm12[/tex]
