2x^2 -12x +p = q(x-r)^2 +10
To simplify and solve for p, we can expand the right side of the equation:
q(x-r)^2 + 10 = qx^2 - 2qxr + qr^2 + 10
Now we can equate the expanded form with the left side of the equation:
2x^2 - 12x + p = qx^2 - 2qxr + qr^2 + 10
To proceed, we will match the terms with the same power of x on both sides:
2x^2 = qx^2
This tells us that q = 2.
The term with x^2 on the left side is 0, while on the right side it is 2qxr. Since qx = 0, we can conclude that rx = 0, which means r = 0.
Now our equation becomes:
2x^2 - 12x + p = 2x^2 + 10
To solve for p, we can subtract 2x^2 from both sides and add 12x to both sides:
-12x + p = 10
Finally, we isolate p by subtracting 10 from both sides:
p = 10 - 12x
Therefore, the simplified form of the equation is p = 10 - 12x.