Question

Solve x2+10x=24 by completing the square. Which is the solution set of the equation?

Answer 1

good, the number in front of the x^2 term is 1
we can move to the next step

take 1/2 of the linear coefient and square it
10 is the linear coefient
10/2=5, (5)^2=25
add that to both sides

x²+10x+25=24+25
factor perfect square trionmial
(x+5)²=49
squaer root both sides
remember to take positive and negative roots
x+5=+/-7
minus 7 both sides
x=-5+/-7
x=-5+7 and -5-7
x=2 annd -12


the 2 soltuions are x=-12 and 2

Answer 2

x^2+10x+25= 24+25

(x+5)^2= 49

x+5= +-7 (plus or minus 7)

x= -7-5
x=-12

x=7-5
x=2

Final answer: x={-12, 2}