Answer:
16
Step-by-step explanation:
To solve this equation, we need the formula for perfect squares:
- [tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
or
- [tex](a - b)^2 = a^2 - 2ab + b^2[/tex] this is the formula we will use because the signs match the one in the question.
Knowing these, we can set up an equation that assumes that the answer we will end up with is a perfect square.
Work:
[tex](v - x)^2 = v^2 -8v + x^2[/tex]
- this is the setup for being able to solve for the unknown [tex]x[/tex], now we need to solve for [tex]x[/tex].
[tex](v - x)^2 = v^2 - 8v + x^2[/tex] (I replaced [tex]2ab[/tex] with [tex]8v[/tex] because I'm setting up this question to be a perfect square).
[tex](v - x) (v - x) = v^2 - 8v + x^2[/tex]
- multiply the left side. Remember that your answer will not be [tex]v^2 + x^2[/tex], but [tex]v^2 - 2vx +x^2[/tex].
[tex]v^2 - 2vx + x^2 = v^2 + 8v + x^2[/tex]
- Divide like terms and isolate the variable. In this case, [tex]v^2[/tex] and [tex]x^2[/tex] are on both sides, so dive them and they will be canceled out.
[tex]2vx = 8v[/tex]
- divide by [tex]2v[/tex] and you will have your value for [tex]x[/tex].
[tex]x = 4[/tex]
- Now we plug [tex]x[/tex] into our original equation equation for perfect squares.
[tex](v - 4)^2 = v^2 - 8v + 16[/tex]
Our final answer is 16.
