Exercise
Factor the quadratic equation
4p^2-21p-18=0
Final Answer
Solution
4p^2-21p-18=0
It’s a quadratic equation. Our equation coefficients are
a=4, b=-21, c=-18
We solve it with the quadratic formula. Putting the coefficients in the formula gives us
p_{1,2}=\frac{21\pm \sqrt{{21}^2-4\cdot 4\cdot (-18)}}{2\cdot 4}=
=\frac{21\pm \sqrt{729}}{8}=
=\frac{21\pm 27}{8}
Hence, we get the solutions:
p_1=\frac{21+27}{8}=6
p_2=\frac{21-27}{8}=-\frac{6}{8}=-\frac{3}{4}
Thus, the factorizing of the quadratic equation is
4p^2-21p-18=
=4(p-6)(p+\frac{3}{4})=
=(p-6)(4p+3)