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

Question

asked Nov 23, 2019 155k views

2 Answers

Grub · Answer 1 · 2019-11-25T04:45:16+0000

Answer:
$x=(7\pm 3i√(3))/(2)$

Step-by-step explanation:

Since, given quadratic function,
(x-5)^2 + 3(x-5) + 9 = 0 -----(1)

let us consider,
x-5=p -----(2)

Put this value in equation (1),

We get,
p^2+3 p+9=0 , which is also a quadratic equation.

Since, quadratic formula for finding the root of quadratic equation of type
ax^2+bx+c=0 is,
$x=\frac{-b\pm√(b^2-4ac)} {2a}$

Here, a=1, b=3 and c=9, so,
$p=\frac{-3\pm√(3^2-4*1 *9)} {2*1}$

Thus,
$p=\frac{-3\pm3√(-3)} {2}$ ⇒
$p=\frac{-3\pm3i√(3)} {2}$ (because √-1=i)

Now, from equation(2)
$x-5=\frac{-3\pm3i√(3)} {2}$

⇒
$x=\frac{-3\pm3i√(3)} {2}+5=(7\pm 3i√(3))/(2)$

⇒
$x=(7\pm 3i√(3))/(2)$