Question

2 STEP PROBLEM: QUADRATIC EQUATION 18x^2 = 21x

Answer 1

`\begin{gathered} Step1\colon\mleft(x\mright)\mleft(18x+21\mright)=0 \\ x=\text{ 0 and x=-7/6} \end{gathered}`

Step-by-step explanation

`18x^2=-21x`

Step 1

to get the form

`ax^2+bx+c=0`

a) add 21 x in both sides

`\begin{gathered} 18x^2=-21x \\ 18x^2+21x=-21x+21x \\ 18x^2+21x=0 \\ so\text{ a=18, b=21, c=0} \end{gathered}`

Step 2

now, factorize the left hand side of the equation

`\begin{gathered} 18x^2+21x=0 \\ (x)(18x+21)=0 \\ so\text{, the factors are x and (18x+21)} \end{gathered}`

now, to get zero from those factors

`\begin{gathered} (x)(18x+21)=0 \\ x=\text{ 0} \\ or \\ 18x+21=0 \\ \text{subtract 21 in both sides} \\ 18x+21-21=0-21 \\ 18x=-21 \\ \text{divide both sides by 18} \\ (18x)/(18)=(-21)/(18) \\ x=-(21)/(18)=-(7)/(6) \\ x=-(7)/(6) \end{gathered}`

so, the answer is

`x=\text{ 0 and x=-7/6}`

I hope this helps you