Answer:
option (d) and (f) is correct.
The solution of given quadratic equation is 3 and -9.
Step-by-step explanation:
Given quadratic equation [tex]x^2+6x=27[/tex]
We have to solve the given quadratic equation using quadratic formula.
Consider [tex]x^2+6x=27[/tex] , we can rewrite it as [tex]x^2+6x-27=0[/tex]
For the general quadratic equation [tex]ax^2+bx+c=0[/tex] the quadratic formula is given as [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a = 1 , b= 6 and c = -27
Substitute, we get,
[tex]x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\left(-27\right)}}{2\cdot \:1}[/tex]
Solving further , we get,
[tex]x_{1,2}=\frac{-6\pm\sqrt{6^2+4\cdot \:1\cdot \:27}}{2\cdot \:1}[/tex]
[tex]x_{1,2}=\frac{-6\pm\sqrt{144}}{2\cdot \:1}[/tex]
We know [tex]\sqrt{144}=12[/tex], we get,
[tex]x_{1,2}=\frac{-6\pm 12}{2\cdot \:1}[/tex]
[tex]x_{1}=\frac{-6+12}{2}[/tex] and [tex]x_{2}=\frac{-6-12}{2}[/tex]
Solving we get,
[tex]x_{1}=\frac{6}{2}[/tex] and [tex]x_{2}=\frac{-18}{2}[/tex]
[tex]x_{1}=3[/tex] and [tex]x_{2}=-9[/tex]
Thus, the solution of given quadratic equation is 3 and -9.
Thus, option (d) and (f) is correct.
