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jeka94
2 years ago
5

What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve.

Mathematics
1 answer:
blondinia [14]2 years ago
7 0

Answer:

Option 2 -  x=\frac{7\pm3\sqrt{3}i}{2}

Step-by-step explanation:

Given : Equation (x-5)^2+3(x-5)+9=0

To find : What is the solution of the equation ?

Solution :

Using substitution method,

Let y=x-5

y^2+3y+9=0

Using quadratic formula, x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here, a=1, b=3 and c=9

y=\frac{-3\pm\sqrt{3^2-4(1)(9)}}{2(1)}

y=\frac{-3\pm\sqrt{-27}}{2}

y=\frac{-3\pm3\sqrt{3}i}{2}

Substitute back,

x=\frac{-3\pm3\sqrt{3}i}{2}+5

x=\frac{-3\pm3\sqrt{3}i+10}{2}

x=\frac{7\pm3\sqrt{3}i}{2}

Therefore, option 2 is correct.

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