Solve for $$ j $$ $$ -2+2 \sqrt{-8 j+9}=8 $$

Question

UpStudy AI · Accepted Answer

To solve the equation for $$ j $$:

$$
-2 + 2 \sqrt{-8j + 9} = 8
$$

**Step 1: Isolate the Square Root**

Start by moving the constant term to the other side:

$$
2 \sqrt{-8j + 9} = 8 + 2
$$
$$
2 \sqrt{-8j + 9} = 10
$$

**Step 2: Solve for the Square Root**

Divide both sides by 2 to isolate the square root:

$$
\sqrt{-8j + 9} = \frac{10}{2}
$$
$$
\sqrt{-8j + 9} = 5
$$

**Step 3: Eliminate the Square Root**

Square both sides to remove the square root:

$$
(\sqrt{-8j + 9})^2 = 5^2
$$
$$
-8j + 9 = 25
$$

**Step 4: Solve for $$ j $$**

Subtract 9 from both sides:

$$
-8j = 25 - 9
$$
$$
-8j = 16
$$

Divide both sides by -8:

$$
j = \frac{16}{-8}
$$
$$
j = -2
$$

**Step 5: Verify the Solution**

Substitute $$ j = -2 $$ back into the original equation to ensure it's valid:

$$
-2 + 2 \sqrt{-8(-2) + 9} = -2 + 2 \sqrt{16 + 9} = -2 + 2 \sqrt{25} = -2 + 2 \times 5 = -2 + 10 = 8
$$

The equation holds true, so the solution is correct.

**Answer:** $$ j = -2 $$
$$ j = -2 $$

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