Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{(x+2)}^{2}={2}^{2}{x}^{2}\]
Simplify \({2}^{2}\) to \(4\).
\[{(x+2)}^{2}=4{x}^{2}\]
Expand.
\[{x}^{2}+4x+4=4{x}^{2}\]
Move all terms to one side.
\[{x}^{2}+4x+4-4{x}^{2}=0\]
Simplify \({x}^{2}+4x+4-4{x}^{2}\) to \(-3{x}^{2}+4x+4\).
\[-3{x}^{2}+4x+4=0\]
Multiply both sides by \(-1\).
\[3{x}^{2}-4x-4=0\]
Split the second term in \(3{x}^{2}-4x-4\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times -4=-12\]
Ask: Which two numbers add up to \(-4\) and multiply to \(-12\)?
Split \(-4x\) as the sum of \(2x\) and \(-6x\).
\[3{x}^{2}+2x-6x-4\]
\[3{x}^{2}+2x-6x-4=0\]
Factor out common terms in the first two terms, then in the last two terms.
\[x(3x+2)-2(3x+2)=0\]
Factor out the common term \(3x+2\).
\[(3x+2)(x-2)=0\]
Solve for \(x\).
Ask: When will \((3x+2)(x-2)\) equal zero?
When \(3x+2=0\) or \(x-2=0\)
Solve each of the 2 equations above.
\[x=-\frac{2}{3},2\]
\[x=-\frac{2}{3},2\]
Decimal Form: -0.666667, 2
x=-2/3,2
