Equation : find values

[DeanBH]

2x^2 − 12x + p = q(x − r)^2 + 10 for all values of x find p q and r

i've got

2(x-3)^2 + p = Q(x-r)^2 + 10

so q = 2 r = 3 and p = 10?

now the answers say that Q = 2 r = 3 and p = 28?

can someone explain how to properly go about doing this equation.

 

[kamerling]

2x^2 − 12x is not the same as 2(x-3)^2

 

[HallsofIvy]

If a polynomial equation is true for all values of x, then "corresponding coefficients"- that is, coefficients multiplying the same powers of x on opposite sides of the equation- must be the same: multiply the square on the right and compare "corresponding coefficients".

 

[DeanBH]

2x^2 − 12x is not the same as 2(x-3)^2

k I've done it now, thx