Answer:
The solution to the equation are x = 5.089 and x = -0.589
Step-by-step explanation:
Given:
x(at the power of 2) = 6 + 9x
To Find:
The solution of the equation = ?
Solution:
The given equation can be written as
=> [tex]2x^2 = 6+9x[/tex]
=>[tex]2x^2-6 -9x=0[/tex]
=>[tex]2x^2-9x-6=0[/tex]
Using the quadratic formula,
[tex]x = \frac{-b\pm \sqrt{(b^2 -4ac}}{2a}[/tex]
where
a= 2
b = -9
c = -6
Substituting these values,
[tex]x = \frac{-(-9)\pm \sqrt{(-9)^2 -4(2)(-6)}}{2(2)}[/tex]
[tex]x = \frac{-(-9)\pm \sqrt{(81) -4(-12)}}{2(2)}[/tex]
[tex]x = \frac{-(-9)\pm \sqrt{81+48}}{4}[/tex]
[tex]x = \frac{-(-9)\pm \sqrt{129}}{4}[/tex]
[tex]x = \frac{-(-9)\pm 11.357}{4}[/tex]
[tex]x = \frac{9 \pm 11.357}{4}[/tex]
[tex]x = \frac{9 + 11.357}{4}[/tex] [tex]x = \frac{9 - 11.357}{4}[/tex]
[tex]x = \frac{20.357}{4}[/tex] [tex]x = \frac{-2.357}{4}[/tex]
x =5.089 x = -0.589
