SOLUTION: I have two questions: 1. Find, rounded to two decimal places, the solution(s) to the equation 0 = 2x3 - 5x + 7. 2. Solve the equation x(x - 2) = 7.

Algebra ->  Graphs -> SOLUTION: I have two questions: 1. Find, rounded to two decimal places, the solution(s) to the equation 0 = 2x3 - 5x + 7. 2. Solve the equation x(x - 2) = 7.      Log On


   



Question 310678: I have two questions:
1. Find, rounded to two decimal places, the solution(s) to the equation 0 = 2x3 - 5x + 7.
2. Solve the equation x(x - 2) = 7.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E3-5x%2B7%29+
Looks like there is a root near x=-2.
f(x)=2x%5E3+-+5x+%2B+7
f'(x)=6x%5E2-5
I used Newton's method to iterate,
x(n+1)=xn-f(xn)/f'(xn)
Starting with x=-2, the solution quickly converge to x=-2.05098 or to two decimal places, highlight_green%28x=-2.05%29
.
.
.
x%28x-2%29=7
x%5E2-2x-7=0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+4-4%2A1%2A%28-7%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+32+%29%29%2F%282%29+
x+=+%282+%2B-+4sqrt%28+2+%29%29%2F%282%29+
x+=+1+%2B-+2sqrt%28+2+%29+