Question

x²+13x/3=42 solve the given equation​

Answer 1

Step-by-step explanation:

You want two numbers, a and b, that multiply to give 42 (a*b = 42) and add to give -13 (a+b = -13).  Since the numbers must add to give a negative number and multiply to give a positive number, they most both be negative.  Let's try some factors of 42:

 

-21 * -2 = 42           -21 + -2 = -23

-14 * -3 = 42           -14 + -3 = -17

-13 * -4 = 42           -13 + -4 = -17

-7 * -6 = 42           -7 + -6 = -13  So this is the answer!

 

x2 - 13x + 42 = (x-7)(x-6)

Answer 2

Answer:

$\displaystyle{\boxed{\red{\sf\:x\:=\:-\:9}}}\sf\:\quad\:OR\:\quad\:\boxed{\red{\sf\:x\:=\:\dfrac{14}{3}}}$

Step-by-step-explanation:

We have to solve a quadratic equation.

The given quadratic equation is $\displaystyle{\sf\:x^2\:+\:\dfrac{13x}{3}\:=\:42}$

Now,

$\displaystyle{\sf\:x^2\:+\:\dfrac{13x}{3}\:=\:42}$

$\displaystyle{\implies\sf\:3x^2\:+\:13x\:=\:42\:\times\:3\:\qquad\dots\:[\:Multiplying\:by\:3\:]}$

$\displaystyle{\implies\sf\:3x^2\:+\:13x\:=\:126}$

$\displaystyle{\implies\sf\:3x^2\:+\:13x\:-\:126\:=\:0}$

$\displaystyle{\implies\sf\:3x^2\:+\:27x\:-\:14x\:-\:126\:=\:0}$

$\displaystyle{\implies\sf\:3x\:(\:x\:+\:9\:)\:-\:14\:(\:x\:+\:9\:)\:=\:0}$

$\displaystyle{\implies\sf\:(\:x\:+\:9\:)\:(\:3x\:-\:14\:)\:=\:0}$

$\displaystyle{\implies\sf\:x\:+\:9\:=\:0\:\quad\:OR\:\quad\:3x\:-\:14\:=\:0}$

$\displaystyle{\implies\sf\:x\:=\:-\:9\:\quad\:OR\:\quad\:3x\:=\:14}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:-\:9}}}\sf\:\quad\:OR\:\quad\:\underline{\boxed{\red{\sf\:x\:=\:\dfrac{14}{3}}}}}$