Question

Please show all work:If f(x) = 2x² + x - 3, find x if f(x) = 25. ​

Answer 1

Hi, there!

To solve the function operation, let's start by writing 25 everywhere we see x:

$\boldsymbol{f(x)=2(25)^2+25-3}$

    ________

Now here's the most important part - The order of operations.

It's vital in simplifying expressions with multiple operations, like this one.

There's an acronym that will help you remember the order of operations.

$\boldsymbol{BODMAS}$

Here,

1. B = Brackets. The first of all these operations, the Brackets operation tells us to simplify all expressions with brackets, if we have any.
2. O = order of exponents. This operation comes right after brackets. Once we've evaluated all the expressions with the brackets, we can start evaluating exponential expressions.
3. D = division & M = multiplication. Unlike the two operations above, these two operations are interchangeable; you can do division first, and then multiplication, or the other way around.
4. A = addition & S=Subtraction. Just like the two operations above, these two guys are also interchangeable.

  _________

Now let's get down to evaluating our expression.

We have

1. Exponents
2. Multiplication
3. Addition
4. Subtraction

         $\boldsymbol{f(25)=2(625)+25-3}$

         $\boldsymbol{f(25)=1,250+25-3}$

                    $\boldsymbol{=1,250+22}$

                    $\boldsymbol{=1,272}$

Hope the answer - and explanation - made sense,

happy studying!!

                                                                                              $\tiny\boldsymbol{frozen \ melody}$

Answer 2

$f(x) = 2x {}^{2} + x - 3 \\ f(x) = 25 \\ 2x {}^{2} + x - 3 = 25 \\ 2x {}^{2} + x - 28 = 0 \\ \\ x_{1} = \frac{ - 1 + \sqrt[]{1 {}^{2} - 4(2)( - 28) } }{2(2)} \\ x_{1} = \frac{ - 1 + 15 }{4} = \frac{14}{4} = 3.5$

$x_{2} = \frac{ - 1 - \sqrt{225} }{4} = \frac{ - 1 - 15}{4} = \frac{ - 16}{4} = - 4$