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Express 2x² - 12x + 7 in the form a (x + b)² + c, where a, b and c are constants.

User Danpalmer
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1 Answer

6 votes

Answer:

2(x-3)² - 11 where a = 2, b = -3, c = -11

Explanation:

Taking the first 2 terms,

2x² - 12x ==> 2(x² -6x) [1]

x² -6x can be rewritten as (x -3)² - 9 [2]

since (x-3)² = x² -6x + 9

Substituting for x² -6x in [1] we get

2(x² -6x) = 2((x -3)² - 9 ) = 2(x-3)² -18

Therefore substituting for 2x² - 12x in the original equation we get

2x² - 12x + 7 = 2(x-3)² -18 + 7 ==> 2(x-3)² -11

this is in the form (a(x+b) + c where a = 2, b = -3 and c= -11

Cross-check
2(x-3)² - 11 ==> 2 (x² -6x +9) -11 ==> 2x² -12x +18 - 11 ==> 2x² -12x + 7

User Liran Funaro
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4.8k points