Which equation has the same solution as x^(2)-18 x-1=-7 ? (x-9)^(2)=75 (x+9)^(2)=-87 (x+9)^(2)=75 (x-9)^(2)=-87

Question

Which equation has the same solution as  x^(2)-18 x-1=-7 ?  (x-9)^(2)=75  (x+9)^(2)=-87  (x+9)^(2)=75  (x-9)^(2)=-87

Bytelearn · Accepted Answer

Simplify the Equation: First, let's simplify the given equation x^(2)-18x-1=-7 by adding 7 to both sides to set it equal to zero. x^(2) - 18x - 1 + 7 = -7 + 7 x^(2) - 18x + 6 = 0Check Option 1: Now, let's look at the first option (x-9)^(2)=75 and expand it to see if it simplifies to the same quadratic equation. (x-9)^(2) = x^(2) - 18x + 81 = 75 Subtract 75 from both sides to set it equal to zero. x^(2) - 18x + 81 - 75 = 0 x^(2) - 18x + 6 = 0 This matches the simplified version of the given equation.Check Option 2: Next, let's look at the second option (x+9)^(2)=-87 and see if it can be a valid solution. Since the square of a real number is always non-negative, (x+9)^(2) cannot equal a negative number like -87. Therefore, this option cannot have the same solution as the given equation.Check Option 3: Now, let's look at the third option (x+9)^(2)=75 and expand it to see if it simplifies to the same quadratic equation. (x+9)^(2) = x^(2) + 18x + 81 = 75 Subtract 75 from both sides to set it equal to zero. x^(2) + 18x + 81 - 75 = 0 x^(2) + 18x + 6 ≠ 0 This does not match the simplified version of the given equation.Check Option 4: Finally, let's look at the fourth option (x-9)^(2)=-87 and see if it can be a valid solution. Similar to the second option, since the square of a real number is always non-negative, (x-9)^(2) cannot equal a negative number like -87. Therefore, this option cannot have the same solution as the given equation.

Which equation has the same solution as $x^{2}-18 x-1=-7$ ? $\newline$ $(x-9)^{2}=75$ $\newline$ $(x+9)^{2}=-87$ $\newline$ $(x+9)^{2}=75$ $\newline$ $(x-9)^{2}=-87$

Full solution

More problems from Solve complex trigonomentric equations

Related topics

Which equation has the same solution as x2−18x−1=−7 x^{2}-18 x-1=-7 x2−18x−1=−7 ?\newline(x−9)2=75 (x-9)^{2}=75 (x−9)2=75\newline(x+9)2=−87 (x+9)^{2}=-87 (x+9)2=−87\newline(x+9)2=75 (x+9)^{2}=75 (x+9)2=75\newline(x−9)2=−87 (x-9)^{2}=-87 (x−9)2=−87

Which equation has the same solution as $x^{2}-18 x-1=-7$ ? $\newline$ $(x-9)^{2}=75$ $\newline$ $(x+9)^{2}=-87$ $\newline$ $(x+9)^{2}=75$ $\newline$ $(x-9)^{2}=-87$