Respuesta :
Answer:
Missing step is "Add and subtract 4 in the parenthesis." The resulted equation is [tex]5=-6(x-2)^2+24[/tex].
Step-by-step explanation:
The given equation is
[tex]0=-6x^2+24x-5[/tex]
Step 1: Add 5 on both sides.
[tex]5=-6x^2+24x[/tex]
Step 2: Taking out 6 as common factor.
[tex]5=-6(x^2-4x)[/tex]
If an expression is defined as [tex]x^2+bx[/tex], then add [tex](\frac{b}{2})^2[/tex] in the expression to make it perfect square.
Here b=-4,
[tex](\frac{b}{2})^2=(\frac{-4}{2})^2=4[/tex]
Step 3: Add and subtract 4 in the parenthesis.
[tex]5=-6(x^2-4x+4-4)[/tex]
[tex]5=-6(x62-4x+4)-6(-4)[/tex]
[tex]5=-6(x-2)^2+24[/tex] [tex][\becasue (a-b)^2=a^2-2ab+b^2][/tex]
Step 4: Subtract 24 from both sides.
[tex]5-24=-6(x-2)^2+24-24[/tex]
[tex]-19=-6(x-2)^2[/tex]
Step 5: Divide both sides by -6.
[tex]\frac{19}{6}=(x-2)^2[/tex]
Step 6: Taking square root on both sides.
[tex]\pm \sqrt{\frac{19}{6}}=(x-2)[/tex]
Step 7: Add 2 on both sides.
[tex]2\pm \sqrt{\frac{19}{6}}=x[/tex]
Therefore, the two solutions are [tex]x=2\pm \sqrt{\frac{19}{6}}[/tex].
The missing step for the given quadratic equation is:
- "Add and subtract 4 in the parenthesis."
Given that the quadratic equation given, we can see that we are given:
[tex]0 = - 6x {}^{2} + 24x - 5[/tex]
Therefore, when we add the missing part which is to add and subtract 4 in the parenthesis, the the quadratic equation can be solved.
This would balance both sides and to find the value of x.
Read more about quadratic equations here:
https://brainly.com/question/1214333
