Easy Solution for x + √x = 90: List of Solutions | Midterm Math Troubles

  • Thread starter MacLaddy
  • Start date
In summary, the student struggled with the first problem on their midterm, which involved solving the equation x + √x = 90 and listing all solutions. They attempted to isolate the radical and create a quadratic equation, but were unable to find solutions that worked. Eventually, they realized their mistake and solved the equation correctly.
  • #1
MacLaddy
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Homework Statement



Okay, so I just got home a few moments ago from the first of two midterms that I will have to take this year, (do the math on that one) and I can not seem to figure out the very first problem that was listed on the test.

It was

x + [tex]\sqrt{x}[/tex] = 90


Homework Equations



It says "List all solutions"

The Attempt at a Solution



I tried several things, but none that seemed to fit correctly. Just by looking at it I can see that one of the solutions is x=81, but I can't get it to spit that out algebraically.

I've isolated the radical, then squared both sides to give myself a quadratic, but when I solve that I get two answers that do not work.

I'm sure this is an easy question, and one that I should know. It will probably wake me up in the middle of the night, but it's driving me crazy for now.
 
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  • #2
Oh good grief... I got it.

I wasn't squaring 90-x together and foiling.

x = (90-x)^2

I was squaring them individually

x = 8100+x^2
 

Related to Easy Solution for x + √x = 90: List of Solutions | Midterm Math Troubles

1. What is the general approach to solving "Easy Solution for x + √x = 90?"

The general approach to solving this problem is to isolate the square root term on one side of the equation, square both sides, and then solve for x. This involves using algebraic manipulation and the rules of exponents.

2. How many solutions does "Easy Solution for x + √x = 90" have?

This equation has two solutions: x = 10 and x = 81.

3. How do I know if my solution for "Easy Solution for x + √x = 90" is correct?

To check if your solution is correct, you can substitute the value of x into the original equation and see if it satisfies the equation. Alternatively, you can graph the equation and see if the solution points lie on the curve.

4. Can I use a calculator to solve "Easy Solution for x + √x = 90?"

Yes, you can use a calculator to solve this equation. However, it is important to understand the steps involved in solving it manually, as calculators can sometimes give incorrect solutions due to rounding errors.

5. Are there any real-life applications of "Easy Solution for x + √x = 90?"

This type of equation can arise in various fields such as finance, engineering, and physics, where solving for unknown variables is necessary. For example, it can be used to calculate interest rates, determine the optimal size of a structure, or find the velocity of a falling object.

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