Answer :
We start with the equation
[tex]$$10v^2 - 8 = 181.$$[/tex]
Step 1: Isolate the term with [tex]$v^2$[/tex].
Add [tex]$8$[/tex] to both sides of the equation:
[tex]$$10v^2 = 181 + 8 = 189.$$[/tex]
Step 2: Solve for [tex]$v^2$[/tex].
Divide both sides of the equation by [tex]$10$[/tex]:
[tex]$$v^2 = \frac{189}{10} = 18.9.$$[/tex]
Step 3: Solve for [tex]$v$[/tex].
Take the square root of both sides. Remember that taking the square root gives two solutions (one positive and one negative):
[tex]$$v = \sqrt{18.9} \quad \text{or} \quad v = -\sqrt{18.9}.$$[/tex]
Using a calculator, we find
[tex]$$\sqrt{18.9} \approx 4.347413023856832,$$[/tex]
so the two solutions are
[tex]$$v \approx 4.347413023856832 \qquad \text{and} \qquad v \approx -4.347413023856832.$$[/tex]
[tex]$$10v^2 - 8 = 181.$$[/tex]
Step 1: Isolate the term with [tex]$v^2$[/tex].
Add [tex]$8$[/tex] to both sides of the equation:
[tex]$$10v^2 = 181 + 8 = 189.$$[/tex]
Step 2: Solve for [tex]$v^2$[/tex].
Divide both sides of the equation by [tex]$10$[/tex]:
[tex]$$v^2 = \frac{189}{10} = 18.9.$$[/tex]
Step 3: Solve for [tex]$v$[/tex].
Take the square root of both sides. Remember that taking the square root gives two solutions (one positive and one negative):
[tex]$$v = \sqrt{18.9} \quad \text{or} \quad v = -\sqrt{18.9}.$$[/tex]
Using a calculator, we find
[tex]$$\sqrt{18.9} \approx 4.347413023856832,$$[/tex]
so the two solutions are
[tex]$$v \approx 4.347413023856832 \qquad \text{and} \qquad v \approx -4.347413023856832.$$[/tex]
