Answer :
The value of Q "option C) 7" is correct option.
Step-by-step explanation:
The given quadratic equation:
[tex]x^2 - 18x +74=0[/tex]
To find, the value of Q = ?
[tex]x^2 - 18x +74=0[/tex]
Adding both sides 81, we get
[tex]x^2 - 18x +81+74=81[/tex]
⇒ [tex]x^2[/tex] - 2(x)8 + [tex]9^2[/tex] = 81 - 74
Using the algebraic identity,
[tex](a-b)^{2} =a^{2} +b^{2} -2ab[/tex]
⇒ [tex](x-9)^{2} =7[/tex] is the form of [tex](x-p)^2 = Q[/tex]
Here, P = 9 and Q = 7
Thus, the value of Q "option C) 7" is correct option.
If the quadratic equation x^2 + 18x +74=0 is rewritten in the form (x-p)²= Q. Then the value of Q is 7.
What is a quadratic equation?
It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Given
The quadratic equation [tex]\rm x^{2} + 18 x + 74 = 0[/tex].
How to find the value of Q?
If the quadratic equation [tex]\rm x^{2} +18x +74=0[/tex] is rewritten in the form
[tex]\rm (x - p)^2 = Q[/tex]
Add and subtract 9² in the equation.
[tex]\rm x^2 + 18x + 9^2 - 9^2 + 74 =0[/tex]
We know the formula
[tex]\rm (a + b)^2 = a^2 + 2ab + b^2[/tex]
Then equation will be
[tex]\begin{aligned} \rm (x + 9)^2 - 81 + 74 &= 0\\\ \ \ \rm (x + 9)^2 - 7 &= 0\end{aligned}[/tex]
Add 7 both the sides, then
[tex]\rm (x + 9 )^2 = 7[/tex]
Thus the value of Q is 7.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981