Respuesta :
Question: What is the solution to the equation [tex]\bold{x\cdot \:2=9x+6}[/tex]
Answer: [tex]\boxed{\bold{x=-\frac{6}{7}}}[/tex]
Explanation: [tex]\downarrow{\downarrow{\downarrow{}}}[/tex]
[ Step One] Subtract 9x From Both Sides Of Equation
[tex]\bold{x\cdot \:2-9x=9x+6-9x}[/tex]
[ Step Two ] Simplify Equation
[tex]\bold{-7x=6}[/tex]
[ Step Three ] Divide Both Sides By -7
[tex]\bold{\frac{-7x}{-7}=\frac{6}{-7}}[/tex]
[ Step Four ] Simplify
[tex]\bold{x=-\frac{6}{7}}[/tex]
[tex]\bold{\rightarrow{}Rhythm \ Bot\leftarrow{}}[/tex]
Answer: The required solutions of the given quadratic equation are
[tex]x=\dfrac{9+\sqrt{105}}{2},~~~\dfrac{9-\sqrt{105}}{2}.[/tex]
Step-by-step explanation: We are given to find the solution of the following quadratic equation :
[tex]x^2=9x+6~~~~~~~\Rightarrow x^2-9x-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the solution of a quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
For the given equation (i), we have
a = 1, b = -9 and c = -6.
Therefore, the solution of equation (i) is as follows :
[tex]x\\\\\\=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\=\dfrac{-(-9)\pm\sqrt{(-9)^2-4\times1\times(-6)}}{2\times1}\\\\\\=\dfrac{9\pm\sqrt{81+24}}{2}\\\\\\=\dfrac{9\pm\sqrt{105}}{2}.[/tex]
Thus, the required solutions of the given quadratic equation are
[tex]x=\dfrac{9+\sqrt{105}}{2},~~~\dfrac{9-\sqrt{105}}{2}.[/tex]
