# How do you solve #x^2 + 5x – 6 = 0#?

The solutions are

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

and

After trying out a few numbers we get :

We now equate factors to zero:

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To solve the quadratic equation ( x^2 + 5x - 6 = 0 ), you can use the quadratic formula:

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

Where ( a = 1 ), ( b = 5 ), and ( c = -6 ).

Substituting these values into the formula:

[ x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 1 \cdot (-6)}}}}{{2 \cdot 1}} ]

[ x = \frac{{-5 \pm \sqrt{{25 + 24}}}}{{2}} ]

[ x = \frac{{-5 \pm \sqrt{{49}}}}{{2}} ]

[ x = \frac{{-5 \pm 7}}{{2}} ]

Therefore, the solutions are ( x = \frac{{-5 + 7}}{{2}} = 1 ) and ( x = \frac{{-5 - 7}}{{2}} = -6 ).

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