Which equation has the same solution as $$ x^{2}+16 x-18=4 $$ ? $$ \begin{array}{l} ext { Answer } \ \begin{array}{l}(x-8)^{2}=86 \ (x-8)^{2}=-42\end{array} \ \left.(x+8)^{2}=-8 ight)^{2}=8\end{array} $$

Question

Which equation has the same solution as $$ x^{2}+16 x-18=4 $$ ? $$ \begin{array}{l}	ext { Answer } \ \begin{array}{l}(x-8)^{2}=86 \ (x-8)^{2}=-42\end{array} \ \left.(x+8)^{2}=-8ight)^{2}=8\end{array} $$

UpStudy AI · Accepted Answer

To find which equation has the same solution as $$ x^{2}+16x-18=4 $$, we first need to simplify the given equation.

1. Start with the original equation:
   $$
   x^{2} + 16x - 18 = 4
   $$

2. Move all terms to one side to set the equation to zero:
   $$
   x^{2} + 16x - 18 - 4 = 0
   $$
   This simplifies to:
   $$
   x^{2} + 16x - 22 = 0
   $$

Now, we will analyze the provided options to see which one is equivalent to this equation.

### Option 1: $$ (x-8)^{2} = 86 $$

Expanding this:
$$
(x-8)^{2} = 86 \implies x^{2} - 16x + 64 = 86 \implies x^{2} - 16x - 22 = 0
$$
This is not equivalent to our equation.

### Option 2: $$ (x-8)^{2} = -42 $$

This equation does not yield real solutions since the square of a real number cannot be negative.

### Option 3: $$ (x+8)^{2} = -8 $$

Similar to option 2, this equation also does not yield real solutions since the square of a real number cannot be negative.

### Option 4: $$ (x+8)^{2} = 8 $$

Expanding this:
$$
(x+8)^{2} = 8 \implies x^{2} + 16x + 64 = 8 \implies x^{2} + 16x + 56 = 0
$$
This is not equivalent to our equation.

### Conclusion

None of the provided options yield the same solution as the original equation $$ x^{2} + 16x - 22 = 0 $$.

Thus, the answer is that none of the equations listed have the same solution as $$ x^{2}+16x-18=4 $$.
None of the provided equations have the same solution as $$ x^{2}+16x-18=4 $$.

Which equation has the same solution as ?

Upstudy AI Solution

Answer

Solution

Option 1:

Option 2:

Option 3:

Option 4:

Conclusion

Beyond the Answer

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