Question

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

Answer 1

(x - 5)2 + 3(x - 5) + 9 = 0

Simplify.

2x - 10 + 3x - 15 + 9 = 0

Add like terms.

(2x + 3x) + (-10 - 15 + 9) = 0

Simplify.

5x + (-34) = 0

5x - 34 = 0

Add 34 to both sides.

5x = 0 + 34

5x = 34

Divide both sides by 5.

x = 34/5

So, x = 6 4/5

~Hope I helped!~

Answer 2

Answer:

The solution of the equation is $x=\frac{7\pm 3i\sqrt{3}}{2},\frac{7\pm 3i\sqrt{3}}{2}$          

Step-by-step explanation:

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

To find : What is the solution of the equation?

Solution :

We have given the expression in quadratic form $ax^2+bx+c=0$

Let $(x-5)=u$ .....(10

The equation form is  $u^2 + 3u + 9 = 0$

The solution of a quadratic formula is, $x=\frac{-b\pm\sqrt{b^2-4ac}} {2a}$

On comparing with general form,

a=1 ,b=3, c=9

Substitute in the formula,

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

$u=\frac{-3\pm\sqrt{9-36}}{2}$

$u=\frac{-3\pm\sqrt{-27}}{2}$

$u=\frac{-3\pm 3\sqrt{3}i}{2}$

$u_1=\frac{-3+3\sqrt{3}i}{2}$

$u_2=\frac{-3-3\sqrt{3}i}{2}$

Substitute in equation (1),

$x-5=u_1$

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

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

$x=\frac{7\pm 3i\sqrt{3}}{2}$

$x-5=u_2$

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

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

$x=\frac{7\pm 3i\sqrt{3}}{2}$

Therefore, The solution of the equation is $x=\frac{7\pm 3i\sqrt{3}}{2},\frac{7\pm 3i\sqrt{3}}{2}$