Question

At which points are the equations y = x2 + 5x - 2 and y = x + 1 equal?

Answer 1

Answer:

When they are equal, y=y, so we can say:

x^2+5x-2=x+1  subtract x from both sides

x^2+4x-2=1  add 2 to both sides

x^2+4x=3, now add half the linear coefficient squared, (4/2)^2=4

x^2+4x+4=3+4 now the left side is a perfect square

(x+2)^2=7  now take the square root of both sides

x+2=±√7  subtract 2 from both sides

x=-2±√7

x=-2+√7 and -2-√7

y=x+1 the two points where these equations are equal are:

(-2-√7, -1-√7) and (-2+√7, -1+√7)

or approximately:

(-4.65, -3.65) and (0.65, 1.65)