Question

X^2+4x+20=12x-5 Solve this equation

Answer 1

Answer:

4 + (or -) 3i

Step-by-step explanation:

Hi!

Alright, so we're going to move all of the variables and constants to one side. Then, using the quadratic formula, we'll find the answer.

1. Move 12x-5 to the left side of the equation by

  a. Subtracting 12x from both sides

  b. adding 5 to both sides.

1: x^2+4x+20-12x+5

2. Group the common terms

  x^2+4x-12x+20+5 --> x^2-8x+25

3. Look at the problem. We can't factor this.

Explanation for why this isn't factorable (you can skip this)

(1) 25 is positive, so its two factors will both be either positive or negative. We're looking for a negative 8, so let's go with negative.

(2) Factors of 25: 1 & 25, 5 &5

Seeing the problem? Ya, none of the factors of 25 sum to eight. So, instead, we're going to use the quadratic formula.

4.  So, the quadratic formula: $\frac{-b+-\sqrt{b^2-4ac} }{2a}$

Our equation is x^2-8x+25=0

a is the constant in front of the x^2

b is the constant in front of the x

c is the term without any x values

so, a=1, b=-8, and c= 25

Into equation:

$\frac{8+-\sqrt{64-4(1)(25)} }{2a}$=$\frac{8+-\sqrt{64-100} }{2}$=$\frac{8+-\sqrt{-36} }{2}$

8/2 = 4

sqrt(-36) = 6i

6i/2 = 3i (remember, we still have the two in the denominator)

4 + (or -) 3i

Answer 2

Answer:

$x=4+ 3\mathbf{i}$

$x=4- 3\mathbf{i}$

Step-by-step explanation:

Solve:

$x^2+4x+20=12x-5$

Move everything to the left side:

$x^2+4x+20-12x+5=0$

Simplify:

$x^2-8x+25=0$

Apply the solver formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Where a=1, b=-8, c=25. Thus:

$\displaystyle x=\frac{8\pm \sqrt{(-8)^2-4(1)(25)}}{2*1}$

$\displaystyle x=\frac{8\pm \sqrt{64-100}}{2}$

$\displaystyle x=\frac{8\pm \sqrt{-36}}{2}$

The solutions are complex numbers:

$\displaystyle x=\frac{8\pm 6\mathbf{i}}{2}$

Simplifying:

$x=4\pm 3\mathbf{i}$

Two solutions are found:

$x=4+ 3\mathbf{i}$

$x=4- 3\mathbf{i}$