To calculate: The solution of the equation x^{2}-5=\left(x+2\right)

Ronnie Baur 2021-11-17 Answered
To calculate: The solution of the equation \(\displaystyle{x}^{{{2}}}-{5}={\left({x}+{2}\right)}{\left({x}-{4}\right)}\).

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Expert Answer

inenge3y
Answered 2021-11-18 Author has 8340 answers
Formula used:
The distributive property is \(\displaystyle{a}{\left({b}+{c}\right)}={a}{b}+{a}{c}\).
Calculation:
Consider the equation \(\displaystyle{x}^{{{2}}}-{5}={\left({x}+{2}\right)}{\left({x}-{4}\right)}\).
Apply the distributive property.
\(\displaystyle{x}^{{{2}}}-{5}={x}^{{{2}}}-{4}{x}+{2}{x}-{8}\)
\(\displaystyle{x}^{{{2}}}-{5}={x}^{{{2}}}-{2}{x}-{8}\)
\(\displaystyle-{5}=-{2}{x}-{8}\)
\(\displaystyle{8}-{5}=-{2}{x}\)
Further solve the equation.
\(\displaystyle{3}=-{2}{x}\)
\(\displaystyle{x}=-{\frac{{{3}}}{{{2}}}}\)
Check the solution \(\displaystyle{x}=-{\frac{{{3}}}{{{2}}}}\) in the equation \(\displaystyle{x}^{{{2}}}-{5}={\left({x}+{2}\right)}{\left({x}-{4}\right)}\).
\(\displaystyle{\left(-{\frac{{{3}}}{{{2}}}}\right)}^{{{2}}}-{5}{\overset{{?}}{{=}}}{\left\lbrace{\left(-{\frac{{{3}}}{{{2}}}}\right)}+{2}\right\rbrace}{\left\lbrace{\left(-{\frac{{{3}}}{{{2}}}}\right)}-{4}\right\rbrace}\)
\(\displaystyle{\frac{{{9}}}{{{4}}}}-{5}{\overset{{?}}{{=}}}{\left({\frac{{-{3}+{4}}}{{{2}}}}\right)}{\left({\frac{{-{3}-{8}}}{{{2}}}}\right)}\)
\(\displaystyle{\frac{{{9}-{20}}}{{{4}}}}{\overset{{?}}{{=}}}{\left({\frac{{{1}}}{{{2}}}}\right)}{\left(-{\frac{{{11}}}{{{2}}}}\right)}\)
\(\displaystyle-{\frac{{{11}}}{{{4}}}}=-{\frac{{{11}}}{{{4}}}}\)
Thus, this solution is true.
Therefore, thesolution of the equation \(\displaystyle{x}^{{{2}}}-{5}={\left({x}+{2}\right)}{\left({x}-{4}\right)}\) is \(\displaystyle{\left\lbrace{3}\right\rbrace}\).
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