Complete the square x^2+10x+24=0

Question

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Answer 1

x^2+10x+24=0

by factoring,

(x+4)(x+6)=0

So, x+4=0 or x+6=0

Therefore, x=-4 or x=-6.

Answer 2

The equation is x² + 10x + 24 = 0

Separate variables and constants aside by adding 64 to each side.

x² + 10x = - 24

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 10. so, (half the x coefficient)² = (10/2)²= 25.

Add 25 to each side

x² + 10x + 25 = - 24 + 25

(x + 5)²= 1

Take square root both sides

x + 5 = ±√1

x = - 5 ± 1

x = - 4, - 6.