If using the method of completing the square to solve the quadratic equation x^2+11x+30=0x 2 +11x+30=0, which number would have to be added to "complete the square"?

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If using the method of completing the square to solve the quadratic equation x^2+11x+30=0x 2 +11x+30=0, which number would have to be added to "complete the square"?

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akiran007 akiran007 · Answer 1 · 2025-03-31T23:35:10-04:00

Answer:

(11/2)² or 121/4 would be added to the equation x ² +11x+30=0, to "complete the square".

Step-by-step explanation:

x 2 +11x+30=0

Write the equation in the form of the square

(x)^2 + 2(x) (11/2) + (11/2)^2 + 30 - 121/4= 0

Square of the first element + 2 into first element into 2nd element + square of 2nd element gives the complete square formula.

How we obtained the second element?

The mid term broken must always be equal to the mid term given.

Hence

2(x) can only be equal to 11x if we multiply it by 11 and divide it with 2.

So the second term must be 11/2 .

To complete the square this second term ( 11/2)² is added and then subtracted to keep the equation equal to the original equation.

(x)^2 + 2(x) (11/2) + (11/2)^2 + 30 - 121/4= 0

Putting it in the form of square

(x+ 11/2)^2 + 120-121/4= 0

Taking LCM and solving

(x+ 11/2)^2 - 1/4= 0

(x+ 11/2)^2 = 1/4

Taking square root on both sides

(x+ 11/2) = ± 1/2

x= - 11/2 ± 1/2

x= -10/2= -5

x= -12/2= -6