Question

Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0

Answer 1

(x +
`(7)/(2)` )² -
`(1)/(4)` = 0

Explanation:

Given

x² + 7x + 12 = 0

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 7x

x² + 2(
`(7)/(2)` )x +
`(49)/(4)` -
`(49)/(4)` + 12 = 0

(x +
`(7)/(2)` )² -
`(49)/(4)` +
`(48)/(4)` = 0 , that is

(x +
`(7)/(2)` )² -
`(1)/(4)` = 0

Answer 2

x^2 + 7x + 12 = 0

x^2 + 7x = -12

(+3)(+4)=0

=−3

=−4

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