Question

show that the equation (x+4)^2=9 can be solved both by factoring and extracting square roots​

Answer 1

Answer:

I have explained the proof below. hope you understand.

Step-by-step explanation:

by factorization,

x²+8x+16=9

x²+8x+7=0

=(x+1)(x+7)=0

x=-1,-7

by extracting square root

x+4=±3

so, x=-1, -7

Answer 2

Answer: Both methods produce the same solutions to the equation (x+4)^2=9.

Step-by-step explanation:

The equation (x+4)^2=9 can be solved both by factoring and extracting square roots.

Factoring: To solve the equation using factoring, we can start by taking the square root of both sides of the equation:

√((x+4)^2)=√9

x+4 = ±3

Now, we can subtract 4 from both sides of the equation to isolate x:

x = ±3 - 4

x = -7 or x = 1

So, x = -7 or x = 1 are the solutions to the equation (x+4)^2=9.

Extracting Square Roots: Another way to solve the equation is to extract the square roots from both sides of the equation:

(x+4) = ±√9

x+4 = ±3

x = ±3 - 4

x = -7 or x = 1

In this case, the solutions are the same as the ones found by factoring: x = -7 or x = 1.

Therefore, both methods produce the same solutions to the equation (x+4)^2=9.

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