Solve for \(x\) in \({x}^{2}+2x-4x-8=0\).
Solve for \(x\).
\[{x}^{2}+2x-4x-8=0\]
Simplify \({x}^{2}+2x-4x-8\) to \({x}^{2}-2x-8\).
\[{x}^{2}-2x-8=0\]
Factor \({x}^{2}-2x-8\).
Ask: Which two numbers add up to \(-2\) and multiply to \(-8\)?
Rewrite the expression using the above.
\[(x-4)(x+2)\]
\[(x-4)(x+2)=0\]
Solve for \(x\).
Ask: When will \((x-4)(x+2)\) equal zero?
When \(x-4=0\) or \(x+2=0\)
Solve each of the 2 equations above.
\[x=4,-2\]
\[x=4,-2\]
\[x=4,-2\]
Substitute \(x=4,-2\) into \({(2x-1)}^{2}-{(x+3)}^{2}=0\).
Start with the original equation.
\[{(2x-1)}^{2}-{(x+3)}^{2}=0\]
Let \(x=4,-2\).
\[{(2\times (4,-2)-1)}^{2}-{((4,-2)+3)}^{2}=0\]
\[{(2\times (4,-2)-1)}^{2}-{((4,-2)+3)}^{2}=0\]
Since \({(2\times (4,-2)-1)}^{2}-{((4,-2)+3)}^{2}=0\) is not true, this is an inconsistent system.
