Math Help - Graphs

1. Graphs

I have the graph showing y=1
_____ , x equals with a cross through 0.
X

How can i use the graph to find approximate roots for the equation 1
___ =2x+3
X

Also how can i rearrange 1
___ =2x+3 to form a quadratic equation?
x
leaving it in the form of P+or - R(in square root)
____________________
r

I am really stuck with this and getting really muddled lol Thank you for your time

2. Originally Posted by Chez_
I have the graph showing y=1
_____ , x equals with a cross through 0.
X

How can i use the graph to find approximate roots for the equation 1
___ =2x+3
X

Also how can i rearrange 1
___ =2x+3 to form a quadratic equation?
x
leaving it in the form of P+or - R(in square root)
____________________
r

I am really stuck with this and getting really muddled lol Thank you for your time
Hi,

draw into the same coordinate system the line $y = 2x+3$ . The x-value(s) of the point of intersection are the solution(s) of the equation.

You have:

$\frac1x = 2x+3$ . Multiply both sides by x which yields:

$1 = 2x^2 + 3x~\iff~2x^2+3x-1=0$ From your answer I assume that you are allowed to use the formula to calculate the solutions:

$x = -\frac{3}{2 \cdot 2} \pm \sqrt{\dfrac{3^2 - 4 \cdot 2 \cdot (-1)}{4 \cdot 2^2 }}$ . Simplify to get: $x = -\frac{3}{4} \pm \sqrt{\dfrac{17}{16 }}= -\frac{3}{4} \pm \frac14 \cdot \sqrt{17}$