im solving nonlinear equations
they are
y = x^2
y - 2 = x
so i plugged in the x^2 to get
x^2 - x = 2
then i factored out an x to get
x(x-1) = 2
now what would i do?
x^2 - x = 2
x^2 - x - 2 = 0
(x-2)(x+1) = 0
Can you take it from here?
yeaa thank youu!!
You're very welcome!
Great job so far! Now, to solve the equation x(x-1) = 2, you can follow these steps:
1. Set the equation equal to zero by subtracting 2 from both sides:
x(x-1) - 2 = 0
2. Expand the equation:
x^2 - x - 2 = 0
3. Now, you have a quadratic equation. To solve it, you can either factor or use the quadratic formula. In this case, let's use factoring.
Think of two numbers whose product is -2 and whose sum is -1. In this case, those numbers are -2 and +1. Rewrite the middle term using these numbers:
x^2 - 2x + x - 2 = 0
4. Group the terms and factor them:
(x^2 - 2x) + (x - 2) = 0
x(x - 2) + 1(x - 2) = 0
(x + 1)(x - 2) = 0
5. Set each factor equal to zero and solve for x:
x + 1 = 0 or x - 2 = 0
x = -1 or x = 2
So the solutions to the equation x(x-1) = 2 are x = -1 and x = 2.
These values represent the x-coordinates of the points of intersection between the two curves y = x^2 and y = x-2.