Please Hurry). Cora is using successive approximations to estimate a positive solution to f (x) = g (x), where f (x) = x^2 + 13 and g (x) =3x + 14. The table shows her results for different input values of x.​

f ( x ) = x^2 + 13

g ( x ) = 3x + 14

f ( x ) = g ( x )

x^2 + 13 = 3x + 14

Subtract sides minus 13

x^2 + 13 - 13 = 3x + 14 - 13

x^2 = 3x + 1

Subtract sides 3x

x^2 - 3x = 3x - 3x + 1

x^2 - 3x = 1

Subtract sides 1

x^2 - 3x - 1 = 1 - 1

x^2 - 3x - 1 = 0

Let's solve this equation for find the values of x .

* Reminder *

First of all we need to find the Delta using the following formula :

ax^2 + bx + c = 0

Delta = b^2 - 4ac

x = - b + delta^1/2 / 2a

..&..

x = - b + delta^1/2 / 2a

x^2 - 3x - 1 = 0

delta = (- 3)^2 - 4 × ( 1 ) × ( - 1 )

delta = 9 + 4

delta = 13

x = - ( - 3) + 13^1/2 / 2 × 1

x = 3 + 3.605 / 2

x = 6.605 / 2

x = 3.3025

x = 3.3 ( the nearest tenth )

..&..

x = - ( - 3) - 13^1/2 / 2 × 1

x = 3 - 3.605 / 2

x = - 0.605 / 2

x = - 0.3025

x = - 0.3 ( the nearest tenth )

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Thus we have two solutions for x which they are :

x = 3.3 ***&*** x = - 0.3

The question asked for the the positive solution so we can just accept x = 3.3

And we're done...