Question

Solve the following quadratic equation using square roots: (x+12)2=9

.(1 point)
Responses

{−7.5,−16.5}
left brace negative 7.5 comma negative 16.5 right brace

{−9,−15}
left brace negative 9 comma negative 15 right brace

{15,9}
left brace 15 comma negative 9 right brace

{−3,−21}

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation (x+12)^2 = 9, first take the square root of both sides:

√((x+12)^2) = √9
x + 12 = ±3

Now solve for x by subtracting 12 from both sides:

x = -12 ± 3

This gives us two possible values for x:

x = -12 + 3 = -9
x = -12 - 3 = -15

So the solution to the quadratic equation is {−9,−15}.

Answer 2

[AI-generated answer — Explain Bot]

To solve the quadratic equation (x+12)^2 = 9 using square roots, you can follow these steps:

Step 1: Rewrite the equation in standard quadratic form:
(x + 12)^2 = 9

Step 2: Take the square root of both sides of the equation to eliminate the square:
√((x + 12)^2) = √9

Step 3: Simplify the square root on the left side:
|x + 12| = 3

Step 4: Now, split the equation into two cases, where the expression inside the absolute value can be positive or negative.

Case 1: x + 12 = 3
Solve for x:
x = 3 - 12
x = -9

Case 2: x + 12 = -3
Solve for x:
x = -3 - 12
x = -15

Therefore, the solutions to the quadratic equation (x+12)^2 = 9 are x = -9 and x = -15, which can be written as {−9, −15}.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To solve the quadratic equation (x + 12)^2 = 9 using square roots, we first take the square root of both sides of the equation.

√((x + 12)^2) = √9

This simplifies to:

x + 12 = ±3

Next, we can separate the equation into two separate equations:

x + 12 = 3 and x + 12 = -3

Now we can solve each equation separately:

For x + 12 = 3:
x = 3 - 12
x = -9

For x + 12 = -3:
x = -3 - 12
x = -15

Therefore, the solutions to the quadratic equation (x + 12)^2 = 9 using square roots are:

{-9, -15}