Simplify \(1+-\frac{\sqrt{1+4x}}{2}\) to \(1-\frac{\sqrt{1+4x}}{2}\).
\[6=1-\frac{\sqrt{1+4x}}{2}\]
Separate terms with roots from terms without roots.
\[6-1=-\frac{\sqrt{1+4x}}{2}\]
Simplify \(6-1\) to \(5\).
\[5=-\frac{\sqrt{1+4x}}{2}\]
Square both sides.
\[25=\frac{1+4x}{4}\]
Multiply both sides by \(4\).
\[25\times 4=1+4x\]
Simplify \(25\times 4\) to \(100\).
\[100=1+4x\]
Subtract \(1\) from both sides.
\[100-1=4x\]
Simplify \(100-1\) to \(99\).
\[99=4x\]
Divide both sides by \(4\).
\[\frac{99}{4}=x\]
Switch sides.
\[x=\frac{99}{4}\]
Check solution
When \(x=\frac{99}{4}\), the original equation \(6=1+-\frac{\sqrt{1+4x}}{2}\) does not hold true.We will drop \(x=\frac{99}{4}\) from the solution set.
