Which equation has the same solution as x^(2)+4x-16=-4 ? (x-2)^(2)=16 (x+2)^(2)=16 (x-2)^(2)=8 (x+2)^(2)=8

Simplify Equation: First, we need to simplify the given equation x^2 + 4x - 16 = -4 by moving all terms to one side to set the equation to zero. x^2 + 4x - 16 + 4 = 0 x^2 + 4x - 12 = 0Factor Quadratic: Now, we need to factor the quadratic equation x^2 + 4x - 12. We look for two numbers that multiply to -12 and add up to 4. These numbers are 6 and -2. (x + 6)(x - 2) = 0Find Solutions: Next, we set each factor equal to zero to find the solutions for x. x + 6 = 0 or x - 2 = 0 So, x = -6 or x = 2Compare with Choices: Now, we need to compare the solutions x = -6 and x = 2 with the choices given to see which equation has the same solutions. The choices are: 1. (x - 2)^2 = 16 2. (x + 2)^2 = 16 3. (x - 2)^2 = 8 4. (x + 2)^2 = 8Analyzing Choice 1: Let's analyze the first choice: (x - 2)^2 = 16. Taking the square root of both sides, we get x - 2 = ±4. So, x = 2 + 4 or x = 2 - 4, which gives us x = 6 or x = -2. This does not match our solutions of x = -6 or x = 2.Analyzing Choice 2: Next, let's analyze the second choice: (x + 2)^2 = 16. Taking the square root of both sides, we get x + 2 = ±4. So, x = -2 + 4 or x = -2 - 4, which gives us x = 2 or x = -6. This matches our solutions of x = -6 or x = 2.No Need to Analyze: We do not need to analyze the third and fourth choices because we have already found a match with the second choice.

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Which equation has the same solution as
x^(2)+4x-16=-4 ?

(x-2)^(2)=16

(x+2)^(2)=16

(x-2)^(2)=8

(x+2)^(2)=8

Which equation has the same solution as $x^{2}+4 x-16=-4$ ? $\newline$ $(x-2)^{2}=16$ $\newline$ $(x+2)^{2}=16$ $\newline$ $(x-2)^{2}=8$ $\newline$ $(x+2)^{2}=8$

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Q. Which equation has the same solution as

x^{2}+4 x-16=-4

\newline

(x-2)^{2}=16

\newline

(x+2)^{2}=16

\newline

(x-2)^{2}=8

\newline

(x+2)^{2}=8

Simplify Equation: First, we need to simplify the given equation $x^2 + 4x - 16 = -4$ by moving all terms to one side to set the equation to zero. $\newline$ $x^2 + 4x - 16 + 4 = 0$ $\newline$ $x^2 + 4x - 12 = 0$
Factor Quadratic: Now, we need to factor the quadratic equation $x^2 + 4x - 12$ . We look for two numbers that multiply to $-12$ and add up to $4$ . These numbers are $6$ and $-2$ . $(x + 6)(x - 2) = 0$
Find Solutions: Next, we set each factor equal to zero to find the solutions for $x$ . $x + 6 = 0$ or $x - 2 = 0$ So, $x = -6$ or $x = 2$
Compare with Choices: Now, we need to compare the solutions $x = -6$ and $x = 2$ with the choices given to see which equation has the same solutions. $\newline$ The choices are: $\newline$ $1$ . $(x - 2)^2 = 16$ $\newline$ $2$ . $(x + 2)^2 = 16$ $\newline$ $3$ . $(x - 2)^2 = 8$ $\newline$ $4$ . $(x + 2)^2 = 8$
Analyzing Choice $1$ : Let's analyze the first choice: x - 2)^2 = 16\. Taking the square root of both sides, we get \$x - 2 = \pm4. So, $x = 2 + 4$ or $x = 2 - 4$ , which gives us $x = 6$ or $x = -2$ . This does not match our solutions of $x = -6$ or $x = 2$ .
Analyzing Choice $2$ : Next, let's analyze the second choice: $(x + 2)^2 = 16$ . Taking the square root of both sides, we get $x + 2 = \pm4$ . So, $x = -2 + 4$ or $x = -2 - 4$ , which gives us $x = 2$ or $x = -6$ . This matches our solutions of $x = -6$ or $x = 2$ .
No Need to Analyze: We do not need to analyze the $3^{rd}$ and $4^{th}$ choices because we have already found a match with the $2^{nd}$ choice.