How do I find two variables in algebra with a given equation?

In summary, the conversation involves a person seeking help with a quadratic equation problem. They mistakenly wrote 125 instead of 25, but the mistake was pointed out by another person. The solution to the problem involves recognizing it as a quadratic equation and using factoring, completing the square, or the quadratic formula to solve for x.
  • #1
GiTS
135
0

Homework Statement


p=-x^2-2x+100 and p=8x+25, find p and x.


Homework Equations





The Attempt at a Solution


-x^2-2x+100=8x+125
-8x -8x
-100 -100
-x^2-10x=-75
x^2+10x=75
/10 /10
1/10x^2+x=75/10 i don't get how to get x alone on one side from here.
 
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  • #2
Try (Ax^2) + Bx + C =0

then you know a formula to get x..
 
  • #3
GiTS said:

Homework Statement


p=-x^2-2x+100 and p=8x+25, find p and x.


Homework Equations





The Attempt at a Solution


-x^2-2x+100=8x+125
-8x -8x
-100 -100
-x^2-10x=-75
x^2+10x=75
/10 /10
1/10x^2+x=75/10 i don't get how to get x alone on one side from here.

Oh, c'mon! That's a quadratic equation. Factor if you can, or complete the square or use the quadratic formula. Oh, by the way, 125- 100= 25, not 75.
 
  • #4
HallsofIvy said:
Oh, c'mon! That's a quadratic equation. Factor if you can, or complete the square or use the quadratic formula. Oh, by the way, 125- 100= 25, not 75.

God I feel stupid. You'd think i'd recognize quadratic equations by now :P. I miswrote 125, supposed to be just 25. Thanks guys!
 
  • #5
No Preblem!


Problem solved :P
 

1. What is the purpose of finding 2 variables in algebra?

Finding 2 variables in algebra allows you to solve a system of equations, where each equation contains 2 different variables. This helps you find the values of both variables simultaneously, which can be useful in real-world applications such as solving for two unknown quantities in a problem.

2. How do I find the solution to a system of equations with 2 variables?

To find the solution, you need to have at least 2 equations with 2 variables each. You can then use algebraic methods such as substitution or elimination to solve for the values of the variables. Once you have found the values, you can check your solution by substituting them back into the original equations.

3. Can a system of equations with 2 variables have more than one solution?

Yes, depending on the equations, a system of equations with 2 variables can have one, infinite, or no solutions. If the lines represented by the equations are parallel, there will be no solution. If the lines intersect at one point, there will be one solution. And if the lines are the same, there will be infinite solutions.

4. How can I graph a system of equations with 2 variables?

To graph a system of equations with 2 variables, you can use the slope-intercept form (y = mx + b) to plot the equations on a coordinate plane. The point(s) where the lines intersect represent the solution to the system of equations.

5. What real-life situations can be represented by a system of equations with 2 variables?

A system of equations with 2 variables can be used to represent various real-life situations, such as finding the cost of two different items with different prices, determining the number of hours needed to complete two different tasks, or calculating the speed of two objects moving at different rates.

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