# How do you solve #x^2 + 8x + 10 = 0#?

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#y = - 8/2 +- (2sqrt2)/2 = -4 +- sqrt6

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To solve the equation ( x^2 + 8x + 10 = 0 ), you can use the quadratic formula, which is given by ( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ), where ( a = 1 ), ( b = 8 ), and ( c = 10 ).

Substitute the values of ( a ), ( b ), and ( c ) into the quadratic formula:

[ x = \frac{{-8 \pm \sqrt{{8^2 - 4(1)(10)}}}}{{2(1)}} ]

Simplify the expression under the square root:

[ x = \frac{{-8 \pm \sqrt{{64 - 40}}}}{2} ] [ x = \frac{{-8 \pm \sqrt{24}}}{2} ]

Now, simplify the square root of 24:

[ x = \frac{{-8 \pm \sqrt{4 \cdot 6}}}{2} ] [ x = \frac{{-8 \pm 2\sqrt{6}}}{2} ]

Divide both terms in the numerator by 2:

[ x = \frac{{-4 \pm \sqrt{6}}}{1} ]

This gives us two solutions:

[ x = -4 + \sqrt{6} ] [ x = -4 - \sqrt{6} ]

So, the solutions to the equation ( x^2 + 8x + 10 = 0 ) are ( x = -4 + \sqrt{6} ) and ( x = -4 - \sqrt{6} ).

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