Solve for \(x\) in \({x}^{2}+2x-3=0\).
Solve for \(x\).
\[{x}^{2}+2x-3=0\]
Factor \({x}^{2}+2x-3\).
Ask: Which two numbers add up to \(2\) and multiply to \(-3\)?
Rewrite the expression using the above.
\[(x-1)(x+3)\]
\[(x-1)(x+3)=0\]
Solve for \(x\).
Ask: When will \((x-1)(x+3)\) equal zero?
When \(x-1=0\) or \(x+3=0\)
Solve each of the 2 equations above.
\[x=1,-3\]
\[x=1,-3\]
\[x=1,-3\]
Substitute \(x=1,-3\) into \(4x(x+7)+10=2({x}^{2}+5)\).
Start with the original equation.
\[4x(x+7)+10=2({x}^{2}+5)\]
Let \(x=1,-3\).
\[4\times (1,-3)\times ((1,-3)+7)+10=2\times ({(1,-3)}^{2}+5)\]
\[4\times (1,-3)\times ((1,-3)+7)+10=2\times ({(1,-3)}^{2}+5)\]
Since \(4\times (1,-3)\times ((1,-3)+7)+10=2\times ({(1,-3)}^{2}+5)\) is not true, this is an inconsistent system.
