(2v-7)^(1/2)=v-3
do this one just like Reiny showed you earlier on
(18-n)^(1/2)=(n/8)^(1/2)
I tried to but I could not get it. Please help me.
ok - first square both sides
(2v-7) = (v-3)^2
2v - 7 = v^2 - 6v + 9
v^2 - 8v + 16 = 0
(v-4)^2 = 0
v = 4
check:
√(8-7) = 4-3
yes
Thank you!
To solve this equation, we'll need to isolate the variable v. Here's how we can do it:
Step 1: Square both sides of the equation to eliminate the square root:
((2v - 7)^(1/2))^2 = (v - 3)^2
Squaring both sides gives us:
2v - 7 = (v - 3)^2
Step 2: Expand the right side of the equation by squaring (v - 3):
2v - 7 = (v - 3)(v - 3)
2v - 7 = (v^2 - 6v + 9)
Step 3: Simplify the equation:
0 = v^2 - 8v + 16
Step 4: Rearrange the equation to be in standard quadratic form:
v^2 - 8v + 16 = 0
Step 5: Factor the quadratic equation:
(v - 4)(v - 4) = 0
Step 6: Solve for v by setting each factor equal to zero:
v - 4 = 0
v = 4
Step 7: Check your answer by substituting the value of v back into the original equation:
(2v - 7)^(1/2) = v - 3
(2(4) - 7)^(1/2) = 4 - 3
(8 - 7)^(1/2) = 1
1 = 1
Therefore, the solution to the equation is v = 4.