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Solve x² + 6x + 7 = 0.x = -1 and x = -5 3+ √2-3+√2-3 ± √22

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ANSWER

[tex]x=-3\pm\sqrt{2}[/tex]

EXPLANATION

We want to solve for x in the equation:

[tex]x^2+6x+7=0[/tex]

To do this, apply the quadratic formula:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

where a = 1, b = 6, c = 7

Therefore, substituting the values of a, b, and c into the formula and solve:

[tex]\begin{gathered} x=\frac{-6\pm\sqrt{6^2-4(1)(7)}}{2(1)}=\frac{-6\pm\sqrt{36-28}}{2} \\ \\ x=\frac{-6\pm\sqrt{8}}{2}=\frac{-6\pm2\sqrt{2}}{2} \\ \\ x=-3\pm\sqrt{2} \end{gathered}[/tex]

That is the solution for x.

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