Question

What are the solutions of the quadratic equation x2=9x+6

Answer 1

Answer:  The required solutions of the given quadratic equation are

$x=\dfrac{9+\sqrt{105}}{2},~~~\dfrac{9-\sqrt{105}}{2}.$

Step-by-step explanation:  We are given to find the solution of the following quadratic equation :

$x^2=9x+6~~~~~~~\Rightarrow x^2-9x-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the solution of a quadratic equation of the form $ax^2+bx+c=0,~a\neq 0$ is given by

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$

For the given equation (i), we have

a = 1,  b = -9  and  c = -6.

Therefore, the solution of equation (i) is as follows :

$x\\\\\\=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\=\dfrac{-(-9)\pm\sqrt{(-9)^2-4\times1\times(-6)}}{2\times1}\\\\\\=\dfrac{9\pm\sqrt{81+24}}{2}\\\\\\=\dfrac{9\pm\sqrt{105}}{2}.$

Thus, the required solutions of the given quadratic equation are

$x=\dfrac{9+\sqrt{105}}{2},~~~\dfrac{9-\sqrt{105}}{2}.$

Answer 2

Question: What is the solution to the equation $\bold{x\cdot \:2=9x+6}$

Answer: $\boxed{\bold{x=-\frac{6}{7}}}$

Explanation: $\downarrow{\downarrow{\downarrow{}}}$

[ Step One] Subtract 9x From Both Sides Of Equation

$\bold{x\cdot \:2-9x=9x+6-9x}$

[ Step Two ] Simplify Equation

$\bold{-7x=6}$

[ Step Three ] Divide Both Sides By -7

$\bold{\frac{-7x}{-7}=\frac{6}{-7}}$

[ Step Four ] Simplify

$\bold{x=-\frac{6}{7}}$

$\bold{\rightarrow{}Rhythm \ Bot\leftarrow{}}$