Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
so the square root of the quatity(x+7)=x-5
so you square both sides and get rid of the square root
x+7=(x-5)^2
(x-5)^2=x^2-10x+25
x+7=x^2-10x+25
subtract 7 from both sides
x=x^2-10x+18
subtract x from both sides
0=x^2-11x+18
so if xy=0 we can assume that x or/and y =0
factor out x^2-11+18
(find what two numbers multiply to get 18 and add to get -11)
-2 times -9=18
-2+(-9)=-11
(x-2)(x-9)=0
set them to zero
x-2=0
x=2
x-9=0
x=9
there are two answers -2 and -9
so you square both sides and get rid of the square root
x+7=(x-5)^2
(x-5)^2=x^2-10x+25
x+7=x^2-10x+25
subtract 7 from both sides
x=x^2-10x+18
subtract x from both sides
0=x^2-11x+18
so if xy=0 we can assume that x or/and y =0
factor out x^2-11+18
(find what two numbers multiply to get 18 and add to get -11)
-2 times -9=18
-2+(-9)=-11
(x-2)(x-9)=0
set them to zero
x-2=0
x=2
x-9=0
x=9
there are two answers -2 and -9
The domain:
The radicand must be greater than or equal to 0.
[tex]x+7 \geq 0 \\ x \geq -7[/tex]
The value of the square root must be greater than or equal to 0.
[tex]x-5 \geq 0 \\ x \geq 0[/tex]
Therefore x≥5.
[tex]\sqrt{x+7}=x-5 \\ (\sqrt{x+7})^2=(x-5)^2 \\ x+7=x^2-10x+25 \\ 0=x^2-11x+18 \\ 0=x^2-9x-2x+18 \\ 0=x(x-9)-2(x-9) \\ 0=(x-2)(x-9) \\ x-2=0 \ \lor \ x-9=0 \\ x=2 \ \lor \ x=9[/tex]
2<5 so it's not a correct solution.
9≥5 so it's a correct solution.
The answer:
x=9
The radicand must be greater than or equal to 0.
[tex]x+7 \geq 0 \\ x \geq -7[/tex]
The value of the square root must be greater than or equal to 0.
[tex]x-5 \geq 0 \\ x \geq 0[/tex]
Therefore x≥5.
[tex]\sqrt{x+7}=x-5 \\ (\sqrt{x+7})^2=(x-5)^2 \\ x+7=x^2-10x+25 \\ 0=x^2-11x+18 \\ 0=x^2-9x-2x+18 \\ 0=x(x-9)-2(x-9) \\ 0=(x-2)(x-9) \\ x-2=0 \ \lor \ x-9=0 \\ x=2 \ \lor \ x=9[/tex]
2<5 so it's not a correct solution.
9≥5 so it's a correct solution.
The answer:
x=9
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.