# Solving a Quadratic Equation with Two Variables

• Ashley1nOnly
In summary, a quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It can be found given two points by solving a system of equations, and the quadratic formula can be used to find the roots of any quadratic equation. There are various methods for finding a quadratic equation from a graph, and an equation can be checked if it is quadratic by looking at the highest exponent or rearranging it into the standard form.
Ashley1nOnly

X^2-yx+y^2-7=0

## Homework Equations

-b +- sqrt(b^2-4ac)/2a

## The Attempt at a Solution

Trying to complete the square with two variables
(x^2-yx)+(y^2)=7

(X^2-yx+y/2)+y^2=7
Where else from here. I'm just having problems because of the y variable

Ashley1nOnly said:

## Homework Statement

X^2-yx+y^2-7=0
What's the complete problem statement? IOW, what are you supposed to do here?
Ashley1nOnly said:

## Homework Equations

-b +- sqrt(b^2-4ac)/2a

## The Attempt at a Solution

Trying to complete the square with two variables
(x^2-yx)+(y^2)=7

(X^2-yx+y/2)+y^2=7
Where else from here. I'm just having problems because of the y variable

The original equation was a differential equation
(2x-y)dx+(2y-X)dy= 0
Which I solved and got
X^2-yx+y^2=7

It took the form of
M(X,y)dx+N(X,y)=0

M(partial y)= N(partial X)

So it had an exact solution
I then continued the rest of the steps and got my final answer but it needs to be in terms of y.

Y=[x+sqrt(28-3x^2)]/2, |x|<sqrt(28/3)

I need help completing the squares so that I can use the quadratic equation to solve for y.

Ashley1nOnly said:
I need help completing the squares so that I can use the quadratic equation to solve for y.
You need y as function of x. So write y2-yx+x2-7 in form (y-x/2)2+f(x)

@Ashley1nOnly, your first post should have started like this:

## Homework Statement

Solve for y in the equation X^2-yx+y^2-7=0

## Homework Equations

-b +- sqrt(b^2-4ac)/2a
One other thing -- what you wrote above would be interpreted by most as
$$-b \pm \frac{\sqrt{b^2 - 4ac}}{2} a$$

Ashley1nOnly said:

X^2-yx+y^2-7=0

## Homework Equations

-b +- sqrt(b^2-4ac)/2a

## The Attempt at a Solution

Trying to complete the square with two variables
(x^2-yx)+(y^2)=7

(X^2-yx+y/2)+y^2=7
Where else from here. I'm just having problems because of the y variable

You have an equation of the form ##y^2 + b y + c = 0##, with appropriate ##b## and ##c##. The solution forms
$$y_1 = \frac{-b + \sqrt{b^2 - 4 c}}{2} , \; y_2 = \frac{-b - \sqrt{b^2 - 4 c}}{2}$$
will give you the answer. It does not matter if ##b,c## are numerical constants, or if they are 1000-page formulas containing 500 other variables; as long as they do not contain ##y##, the quadratic solution formula holds and you are good to go.

Last edited:

## 1. What is a quadratic equation?

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is a second-degree polynomial, meaning the highest exponent is 2.

## 2. How do you find the quadratic equation given two points?

To find the quadratic equation given two points, you can plug the coordinates of the points into the general form of a quadratic equation (y = ax^2 + bx + c). This will give you a system of two equations with three variables. By solving the system, you can find the specific values for a, b, and c, and thus determine the quadratic equation.

## 3. What is the quadratic formula?

The quadratic formula is a formula used to solve quadratic equations. It is written as x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. This formula can be used to find the roots (or solutions) of any quadratic equation.

## 4. What are the different methods for finding a quadratic equation from a graph?

There are several methods for finding a quadratic equation from a graph, including finding the x-intercepts (or roots), using the axis of symmetry, and using the vertex form of a quadratic equation. The most common method is to find the x-intercepts, as these points can be easily read from the graph and used to create the general form of a quadratic equation.

## 5. How can I check if a given equation is a quadratic equation?

To check if an equation is a quadratic equation, you can look at the highest exponent of the variables. If it is 2, then the equation is quadratic. Additionally, you can rearrange the equation into the standard form (ax^2 + bx + c = 0) and check if the coefficients a, b, and c are constants.

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