Separate terms with roots from terms without roots.
\[\sqrt{2-7x}=2x\]
Square both sides.
\[2-7x=4{x}^{2}\]
Move all terms to one side.
\[2-7x-4{x}^{2}=0\]
Multiply both sides by \(-1\).
\[4{x}^{2}+7x-2=0\]
Split the second term in \(4{x}^{2}+7x-2\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[4\times -2=-8\]
Ask: Which two numbers add up to \(7\) and multiply to \(-8\)?
Split \(7x\) as the sum of \(8x\) and \(-x\).
\[4{x}^{2}+8x-x-2\]
\[4{x}^{2}+8x-x-2=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[4x(x+2)-(x+2)=0\]
Factor out the common term \(x+2\).
\[(x+2)(4x-1)=0\]
Solve for \(x\).
Ask: When will \((x+2)(4x-1)\) equal zero?
When \(x+2=0\) or \(4x-1=0\)
Solve each of the 2 equations above.
\[x=-2,\frac{1}{4}\]
\[x=-2,\frac{1}{4}\]
Check solution
When \(x=-2\), the original equation \(\sqrt{2-7x}-2x=0\) does not hold true.We will drop \(x=-2\) from the solution set.
Therefore,
Decimal Form: 0.25
x=1/4
