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Numerade Educator

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Problem 19 Medium Difficulty

Use Newton's method to find all solutions of the equation correct to six decimal places.

$ 2^x = 2 - x^2 $

Answer

$x=-1.257691,0.653483$

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Video Transcript

the first thing I could do in order to use Mittens method is to find the derivative, which is gonna be two to the power of axe times natural log with two plus two x. Okay, now that we got this, we know that if we use a graph recon, see that we can look at our estimates of the zeroes is negative. 1.2 is the estimate of our 1st 0 Therefore, we noted, if acts, it's negative one point to an ex minister to the X minus two plus X squared over to the axe natural of two plus two acts. So overall, we can conclude that we end up with negative 1.257 approximately. And then for our second axe looking at 0.8 putting into the equation, we get zero point 66 million, 0.66 and we get 0.65 1,000,000 0.65 and we get 0.65 which means our two exes are gonna be negative. 1.25 7691 and 0.653 for a three