Which equation has the same solution as x^(2)-8x-12=7 ? (x-4)^(2)=35 (x+4)^(2)=3 (x+4)^(2)=35 (x-4)^(2)=3

Question

Which equation has the same solution as  x^(2)-8x-12=7 ?  (x-4)^(2)=35  (x+4)^(2)=3  (x+4)^(2)=35  (x-4)^(2)=3

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Simplify Equation: Simplify the given equation by moving all terms to one side to set the equation to zero. x^2 - 8x - 12 - 7 = 0 x^2 - 8x - 19 = 0Check First Choice: Look at the first choice (x - 4)^2 = 35 and expand it to see if it matches the simplified equation. (x - 4)^2 = x^2 - 8x + 16 This does not match the simplified equation x^2 - 8x - 19 because the constant term is different (+16 instead of -19).Check Second Choice: Look at the second choice (x + 4)^2 = 3 and expand it to see if it matches the simplified equation. (x + 4)^2 = x^2 + 8x + 16 This does not match the simplified equation x^2 - 8x - 19 because the sign of the x term is different (+8x instead of -8x) and the constant term is different (+16 instead of -19).Check Third Choice: Look at the third choice (x + 4)^2 = 35 and expand it to see if it matches the simplified equation. (x + 4)^2 = x^2 + 8x + 16 This does not match the simplified equation x^2 - 8x - 19 because the sign of the x term is different (+8x instead of -8x) and the constant term is different (+16 instead of -19).Check Fourth Choice: Look at the fourth choice (x - 4)^2 = 3 and expand it to see if it matches the simplified equation. (x - 4)^2 = x^2 - 8x + 16 This does not match the simplified equation x^2 - 8x - 19 because the constant term is different (+16 instead of -19).Adjust First Choice: Since none of the choices match the simplified equation x^2 - 8x - 19 when expanded, we need to check if any of the choices can be transformed to match the simplified equation by moving terms around. Let's add 19 to both sides of the first choice to see if it matches the simplified equation: (x - 4)^2 = 35 (x - 4)^2 + 19 = 35 + 19 x^2 - 8x + 16 + 19 = 54 x^2 - 8x + 35 = 54 This does not match the simplified equation x^2 - 8x - 19.Adjust Second Choice: Add 19 to both sides of the second choice to see if it matches the simplified equation: (x + 4)^2 = 3 (x + 4)^2 + 19 = 3 + 19 x^2 + 8x + 16 + 19 = 22 x^2 + 8x + 35 = 22 This does not match the simplified equation x^2 - 8x - 19.Adjust Third Choice: Add 19 to both sides of the third choice to see if it matches the simplified equation: (x + 4)^2 = 35 (x + 4)^2 + 19 = 35 + 19 x^2 + 8x + 16 + 19 = 54 x^2 + 8x + 35 = 54 This does not match the simplified equation x^2 - 8x - 19.Adjust Fourth Choice: Add 19 to both sides of the fourth choice to see if it matches the simplified equation: (x - 4)^2 = 3 (x - 4)^2 + 19 = 3 + 19 x^2 - 8x + 16 + 19 = 22 x^2 - 8x + 35 = 22 Subtract 22 from both sides to get the simplified equation: x^2 - 8x + 35 - 22 = 0 x^2 - 8x + 13 = 0 This does not match the simplified equation x^2 - 8x - 19.Correct Approach: Realize that a mistake was made in the previous steps. The correct approach is to compare the given equation x^2 - 8x - 12 = 7 with the choices by first bringing the equation to the form x^2 - 8x = 19 (by adding 12 to both sides and then subtracting 7 from both sides). Then, we should look for a choice that, when simplified, has the form x^2 - 8x = 19.

Which equation has the same solution as $x^{2}-8 x-12=7$ ? $\newline$ $(x-4)^{2}=35$ $\newline$ $(x+4)^{2}=3$ $\newline$ $(x+4)^{2}=35$ $\newline$ $(x-4)^{2}=3$

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Which equation has the same solution as x2−8x−12=7 x^{2}-8 x-12=7 x2−8x−12=7 ?\newline(x−4)2=35 (x-4)^{2}=35 (x−4)2=35\newline(x+4)2=3 (x+4)^{2}=3 (x+4)2=3\newline(x+4)2=35 (x+4)^{2}=35 (x+4)2=35\newline(x−4)2=3 (x-4)^{2}=3 (x−4)2=3

Which equation has the same solution as $x^{2}-8 x-12=7$ ? $\newline$ $(x-4)^{2}=35$ $\newline$ $(x+4)^{2}=3$ $\newline$ $(x+4)^{2}=35$ $\newline$ $(x-4)^{2}=3$