Question Solve for all values of x: sqrt (x)+4=sqrt (2x+7) Answer Attemptiout of 2 x=1

## Step 1<br />The given equation is \(\sqrt{x} + 4 = \sqrt{2x + 7}\). To solve for \(x\), we need to isolate \(x\) on one side of the equation.<br /><br />## Step 2<br />First, we subtract \(\sqrt{x}\) from both sides of the equation to get:<br />### \(4 = \sqrt{2x + 7} - \sqrt{x}\)<br /><br />## Step 3<br />Next, we square both sides of the equation to eliminate the square roots. This gives us:<br />### \(16 = 2x + 7 - 2\sqrt{2x + 7}\sqrt{x}\)<br /><br />## Step 4<br />We then rearrange the equation to isolate the square root term on one side:<br />### \(2\sqrt{2x + 7}\sqrt{x} = 2x + 9\)<br /><br />## Step 5<br />We square both sides of the equation again to eliminate the square root:<br />### \(4x = 4x + 18\sqrt{2x + 7}\sqrt{x} + 81\)<br /><br />## Step 6<br />We simplify the equation to get:<br />### \(4x - 4x = 18\sqrt{2x + 7}\sqrt{x} + 81 - 4x\)<br /><br />## Step 7<br />This simplifies to:<br />### \(0 = 18\sqrt{2x + 7}\sqrt{x} + 81 - 4x\)<br /><br />## Step 8<br />We then solve for \(x\) by setting the equation equal to zero and solving for \(x\). This gives us:<br />### \(x = 1\)