Answer :
Answer:
(-12, -2)
Step-by-step explanation:
Rearrange the equation --> x^2 + 14x + 24 = 0
Split 14x into 12x + 2x --> x^2 + 12x + 2x + 24 = 0
Group --> x(x + 12) + 2(x + 12) = 0, (x + 12)(x + 2) = 0
Find roots:
x + 12 = 0, x = -12
x + 2 = 0, x = -2
The solution of the given expression [tex]\rm x^{2} +14x = -24\\[/tex] by completing the square method is 12 and -2.
The given expression is
[tex]\rm x^{2} +14x = -24\\[/tex]
What is completing the square method?
In completing the square, we take half of the coefficient of the middle term and then square it. Then we add it to both sides of the equation
Here coefficient of middle term x is +14.
So, 14/2 = 7
square of 7 is 49
[tex]\rm x^{2} +14x +49= -24+49\\\rm (x+7) (x+7)=25\\\rm (x+7)^{2} =5^{2} \\\rm x+7 =5[/tex]
x+7 = 5 and x+7 = -5
Solve for x by subtracting 7 on both sides
x = -2 and x= -12
Solution set is {-12, -2}
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