Question

Please show all work:

If f(x) = 2x² + x - 3, find x if f(x) = 25.

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Answer 1

`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) = ( - 1 + 15 )/(4) = (14)/(4) = 3.5`

`x_(2) = ( - 1 - √(225) )/(4) = ( - 1 - 15)/(4) = ( - 16)/(4) = - 4 \\`

Answer 2

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}`

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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.

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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}`