Solve Quadratic Equations for x: Mechanics Notes & Error Check

In summary, the conversation was about a quadratic equation that was supposed to equal 3, but the result was either 3 or 2.12 depending on the calculations. However, it was discovered that there was a mistake in the notes and the correct solutions were actually x=4.604 or x=7.984.
  • #1
RStars
7
0
Hey,

I was going through some mechanics notes and came across this quadratic equation to solve for x. In my notes it is supposed to equal 3 however I do not get that result. I am not sure if I am simplifying it wrong or what. I am ending up with 2.12 for the positive value. Please let me know if you get 3 or 2.12 so that I know if the error is in my calculations or in my notes.

http://img707.imageshack.us/img707/338/codecogseqno.gif [Broken]

Thanks in advanced.
 
Last edited by a moderator:
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  • #2
RStars said:
Hey,

I was going through some mechanics notes and came across this quadratic equation to solve for x. In my notes it is supposed to equal 3 however I do not get that result. I am not sure if I am simplifying it wrong or what. I am ending up with 2.12 for the positive value. Please let me know if you get 3 or 2.12 so that I know if the error is in my calculations or in my notes.

http://img707.imageshack.us/img707/338/codecogseqno.gif [Broken]

Thanks in advanced.



It must be some mistake in your notes: if you put [itex]x=3[/itex] in the given eq., one gets that the LHS is not an integer

whereas the RHS is...

DonAntonio
 
Last edited by a moderator:
  • #3
Neither 3 nor 2.12 are roots of the equation as you wrote it.
 
  • #4
3 is correct if the LHS is amended to contain 144x2 rather than 144 + x2.
 
  • #5
um... I haven't done this in a while so forgive me for being simple... but that's not an equation.

if you put x=10 you end up with the equation 122=900, which isn't true.

There's been some kind of mistake.
 
  • #6
evilbrent said:
um... I haven't done this in a while so forgive me for being simple... but that's not an equation.

if you put x=10 you end up with the equation 122=900, which isn't true.

There's been some kind of mistake.



No, that is too an equation. To solve it means to find out the numerical values of x that when substituted in the equation give

a true equality. What you've shown above is that the numerical value x = 10 is not (one of the) a solution(s) of the equation.

DonAntonio
 
  • #7
oh, ok, yes. Sorry engineering maths was a decade ago for me. It's amazing how quickly the knowledge vanishes.

I reduced the original equation down to 0=-71.5x^2+900x-2628 and got 0=(x-4.604)*(x-7.984)
 

What is a quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains a variable raised to the power of 2. It can be written in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

What is the purpose of solving quadratic equations?

The purpose of solving quadratic equations is to find the values of the variable that make the equation true. This can help with real-life problems such as finding the maximum or minimum value of a function, determining the trajectory of a projectile, or finding the roots of a polynomial.

What are the different methods for solving quadratic equations?

There are several methods for solving quadratic equations, including factoring, completing the square, using the quadratic formula, and graphing. Each method has its advantages and is useful for different types of equations.

How do I know if a quadratic equation has real solutions?

A quadratic equation will have real solutions if its discriminant, b^2 - 4ac, is greater than or equal to 0. If the discriminant is less than 0, the equation will have complex solutions.

What are some real-life applications of quadratic equations?

Quadratic equations can be used in various fields such as physics, engineering, and economics. They can help with predicting the motion of projectiles, determining the optimal shape for a bridge, and analyzing business revenue and profit. They are also used in everyday tasks such as calculating the area of a rectangular garden or finding the best fit for a parabolic satellite dish.

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