Which equation has the same solution as x^(2)+14 x+20=8 ? (x-7)^(2)=37 (x-7)^(2)=-61 (x+7)^(2)=37 (x+7)^(2)=-61

Question

Which equation has the same solution as  x^(2)+14 x+20=8 ?  (x-7)^(2)=37  (x-7)^(2)=-61  (x+7)^(2)=37  (x+7)^(2)=-61

Bytelearn · Accepted Answer

Simplify the equation: First, let's simplify the given equation x^(2)+14x+20=8 by moving all terms to one side to set the equation to zero. x^(2) + 14x + 20 - 8 = 0 x^(2) + 14x + 12 = 0Factor the quadratic equation: Now, we need to factor the quadratic equation x^(2) + 14x + 12. (x + 2)(x + 6) = 0Find solutions for x: Next, we find the solutions for x by setting each factor equal to zero. x + 2 = 0 or x + 6 = 0 x = -2 or x = -6Compare with given options: Now, let's compare the solutions x = -2 and x = -6 with the options given. We need to find which equation has the same solutions. We will start with the first option: (x-7)^(2)=37. Let's solve for x. (x - 7)^2 = 37 Take the square root of both sides. x - 7 = ±√37 x = 7 ± √37 This does not match our solutions of x = -2 or x = -6.Check first option: Next, we check the second option: (x-7)^(2)=-61. Since the square of a real number cannot be negative, this equation has no real solutions. This does not match our solutions of x = -2 or x = -6.Check second option: Now, we check the third option: (x+7)^(2)=37. Let's solve for x. (x + 7)^2 = 37 Take the square root of both sides. x + 7 = ±√37 x = -7 ± √37 This does not match our solutions of x = -2 or x = -6.Check third option: Finally, we check the fourth option: (x+7)^(2)=-61. Similar to the second option, this equation has no real solutions because the square of a real number cannot be negative. This does not match our solutions of x = -2 or x = -6.

Which equation has the same solution as $x^{2}+14 x+20=8$ ? $\newline$ $(x-7)^{2}=37$ $\newline$ $(x-7)^{2}=-61$ $\newline$ $(x+7)^{2}=37$ $\newline$ $(x+7)^{2}=-61$

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Which equation has the same solution as x2+14x+20=8 x^{2}+14 x+20=8 x2+14x+20=8 ?\newline(x−7)2=37 (x-7)^{2}=37 (x−7)2=37\newline(x−7)2=−61 (x-7)^{2}=-61 (x−7)2=−61\newline(x+7)2=37 (x+7)^{2}=37 (x+7)2=37\newline(x+7)2=−61 (x+7)^{2}=-61 (x+7)2=−61

Which equation has the same solution as $x^{2}+14 x+20=8$ ? $\newline$ $(x-7)^{2}=37$ $\newline$ $(x-7)^{2}=-61$ $\newline$ $(x+7)^{2}=37$ $\newline$ $(x+7)^{2}=-61$