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For all values of x , x 2 + 6 x − 2 = ( x + p ) 2 + q Find the value of p and the value of q .

User Tlvs
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1 Answer

6 votes

Answer:

p = 3 and q = 7

Explanation:

Given the equation x^2 + 6 x − 2 = ( x + p )^2 + q we are to find the value of p and the value of q .

x^2 + 6 x − 2 = ( x + p )^2 + q

Using the completing the square method on x^2 + 6 x − 2

x^2 + 6 x − 2

= x^2+6x+ 9 - 2 + 9

= (x^2+3x+3x+9)+7

= x(x+3)+3(x+3) + 7

= (x+3)(x+3)+7

= (x+3)^2+7

Compare to the right hand side

(x+3)^2+7 = ( x + p )^2 + q

p = 3 and q = 7

User Maxime Pacary
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