Proximate the solutions to the given equations to the nearest hundreth.?

Question

I'm not asking for answers here, just how I set these up correctly to arrive at the answers. Thanks

1) x^3 = 15x^2 + 88x + 100 (3 solutions)

2) square root(x) + square root (x+1) = x (1 solution)

Answer 1

set equations equal to zero then factor and solve
ti-83 calculator will give solutions,or roots in graphing function.

Answer 2

1) x^3 = 15x^2 + 88x + 100 - u could use a formula
2) try to put in square the whole equation , and than simplyfy it : x+2sqr(x)sqr(x+1)=x^2 ...

Answer 3

x^3 = 15x^2 + 88x + 100
x^3 -15x^2-88x-100 = 0
Decarte's rule of signs says you have one positive root and 2 negative roots. By inspection you can see that one root - close to -3, one is close to -1.6 and one is close to 19.5.
Now use Newton's method to get the degree of accuracy you want.

sqrt(x)+sqrt(x+1)=x
x +2sqrt(x)*sqrt(x+1) + x = x^2
2sqrt(x)*sqrt(x+1)= x^2-2x
4x^2+4 = x^4 -4x^3 +2x^2
x^4 -4x^3 -2x^2 -4=0
Once again there can only be one positive root and inspection shows it to be around 4.68
Use Newtons method to get desired degree of accuracy.

Answer 4

I was able to find a cubic equation calculator and a quadratic
equation calculator by Searching the Web.

Give it a try.