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What number must you add to complete the square ? x^2-18x=29

User Fmark
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2 Answers

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x^2 - 18x + ( (18)/(2))^2 =29 + ( (18)/(2))^2


x^2 - 18x + (9)^2 =29 + (9)^2


(x - 9)^2 = 119

The number to add is 9² which is 81.

Answer: 81
User Radhika
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Answer: The required number to be added is 81.

Step-by-step explanation: We are given to find the number that must be added to both sides of the equation below to complete the square.


x^2-18x=29~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Completing the square means adding a suitable number to an expression such that is becomes a perfect square trinomial.

We have from equation (i) that


x^2-18x=29\\\\\Rightarrow x^2-* x*9=29\\\\\Rightarrow x^2-2* x* 9+9^2=29+9^2\\\\\Rightarrow (x+9)^2=29+81\\\\\Rightarrow (x+9)^2=110.

Thus, the required number to be added is 81.

User Ferroao
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