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36{x}^{2}-49{y}^{2}-6x-7y36x2−49y2−6x−7y
1
In general, given a{x}^{2}+bx+cax2+bx+c, the factored form is:
a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})a(x−2a−b+√b2−4ac)(x−2a−b−√b2−4ac)
2
In this case, a=36a=36, b=-6b=−6 and c=-49{y}^{2}-7yc=−49y2−7y
36(x-\frac{6+\sqrt{{(-6)}^{2}-4\times 36(-49{y}^{2}-7y)}}{2\times 36})(x-\frac{6-\sqrt{{(-6)}^{2}-4\times 36(-49{y}^{2}-7y)}}{2\times 36})36(x−2×366+√(−6)2−4×36(−49y2−7y))(x−2×366−√(−6)2−4×36(−49y2−7y))
3
Simplify
36(x-\frac{6+6\sqrt{1+28y(7y+1)}}{72})(x-\frac{6-6\sqrt{1+28y(7y+1)}}{72})36(x−726+6√1+28y(7y+1))(x−726−6√1+28y(7y+1))
4
Factor out the common term 66
36(x-\frac{6(1+\sqrt{1+28y(7y+1)})}{72})(x-\frac{6-6\sqrt{1+28y(7y+1)}}{72})36(x−726(1+√1+28y(7y+1)))(x−726−6√1+28y(7y+1))
5
Simplify \frac{6(1+\sqrt{1+28y(7y+1)})}{72}726(1+√1+28y(7y+1)) to \frac{1+\sqrt{1+28y(7y+1)}}{12}121+√1+28y(7y+1)
36(x-\frac{1+\sqrt{1+28y(7y+1)}}{12})(x-\frac{6-6\sqrt{1+28y(7y+1)}}{72})36(x−121+√1+28y(7y+1))(x−726−6√1+28y(7y+1))
6
Factor out the common term 66
36(x-\frac{1+\sqrt{1+28y(7y+1)}}{12})(x-\frac{6(1-\sqrt{1+28y(7y+1)})}{72})36(x−121+√1+28y(7y+1))(x−726(1−√1+28y(7y+1)))
7
Simplify \frac{6(1-\sqrt{1+28y(7y+1)})}{72}726(1−√1+28y(7y+1)) to \frac{1-\sqrt{1+28y(7y+1)}}{12}121−√1+28y(7y+1)
36(x-\frac{1+\sqrt{1+28y(7y+1)}}{12})(x-\frac{1-\sqrt{1+28y(7y+1)}}{12})36(x−121+√1+28y(7y+1))(x−121−√1+28y(7y+1))
Done
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