Answer:
[tex](X+10)^2 = 106[/tex]
Step-by-step explanation:
To convert the quadratic equation [tex]X^2+20x-6=0[/tex] into the form [tex](x-p)^2=q[/tex], we need to complete the square. Let's go through this step-by-step:
First, let's start with our equation:
[tex]X^2+20x-6=0[/tex]
Move the constant term to the right side of the equation:
[tex]X^2+20x = 6[/tex]
To complete the square, we take half of the coefficient of x, square it, and add and subtract it from both sides:
Half of 20 is 10, and [tex]10^2 = 100[/tex]
[tex]X^2+20x+100 = 6+100[/tex]
Simplify the right side:
[tex]X^2+20x+100 = 106[/tex]
The left side is now a perfect square trinomial:
[tex](X+10)^2 = 106[/tex]
This is almost in[tex](x-p)^2=q[/tex] form. We just need to adjust it slightly:
[tex](X-(-10))^2 = 106[/tex]
Therefore, in [tex](x-p)^2=q[/tex] form, the equation [tex]X^2+20x-6=0[/tex] becomes:
[tex](X+10)^2 = 106[/tex]
Where [tex]p = -10[/tex] and [tex]q = 106[/tex]
