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Solve each quadratic equation.f(x) = (x + 7)2 – 2

Sagot :

[tex]f(x)=(x+2)^2-2[/tex]

Let's find the solutions:

[tex]\begin{gathered} f(x)=0 \\ \mleft(x+7\mright)^2-2=0 \end{gathered}[/tex]

Solve for x:

Add 2 to both sides:

[tex]\begin{gathered} (x+7)^2-2+2=0+2 \\ (x+7)^2=2 \end{gathered}[/tex]

Take the square root of both sides:

[tex]\begin{gathered} \sqrt[]{(x+7)^2}=\pm\sqrt[]{2} \\ x+7=\pm\sqrt[]{2} \end{gathered}[/tex]

Subtract 7 from both sides:

[tex]\begin{gathered} x+7-7=\pm\sqrt[]{2}-7 \\ x=\pm\sqrt[]{2}-7 \\ so\colon \\ x=\sqrt[]{2}-7\approx5.586 \\ x=-\sqrt[]{2}-7\approx-8.414 \end{gathered}[/tex]

You can verify the results using the graph:

View image SalmaanZ701512
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