How do I manipulate the top equation to become the bottom equation? This gives u

Question

How do I manipulate the top equation to become the bottom equation?

This gives us of x_f = x_ic + v_ic, x^t + 1/2 a_cx t^2 = 1/2 a_cx (x_f - x_it/u_tx) have some algebra ahead of us. First of all, the good news: We now have a one unknown: x_f (which is exactly what we wanted!). The bad news is the bra, we see that this is a quadratic equation in x_f. We'll show a couple of steps should make sure that you can sit down and understand what is done here. u won't get anything this messy on a test, but you must make sure that you u cause this type of thinking you will need on the test!) is buried inside the squared term in the right-hand side of the equation, as well and side, we first multiply out the square in the equation above, and then multiple by 2v_tx^2 We then get the following equation (after some rearrangement) (a_cx)x_f^2 + (-2a_cx x_it - 2v_tx^2) x_f + (a_cx x_it^2) = 0

Explanation / Answer

given:

xf=0.5*acx*((xf-xit)/vtx)^2

==>2*xf*vtx^2=acx*(xf^2+xit^2-2*xf*xit)

==>acx*xf^2+acx*xit^2-2*acx*xf*xit-2*xf*vtx^2=0

==>acx*xf^2+(-2*acx*xit-2*vtx^2)*xf+(acx*xit^2)=0

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