Question

Show work solve x^2-6x= -25

Answer 1

Answer: x = 3 ± 4i

Step-by-step explanation:

 x² - 6x + 25 = 0

a=1  b= -6  c=25

Use Quadratic Formula:

$x = \frac{-b +/- \sqrt{b^{2}-4ac}}{2a}$

$= \frac{-(-6) +/- \sqrt{(-6)^{2}-4(1)(25)}}{2(1)}$

$= \frac{6 +/- \sqrt{36-100}}{2}$

$= \frac{6 +/- \sqrt{-64}}{2}$

$= \frac{6 +/- 8i}{2}$

$= \frac{2(3 +/- 4i)}{2}$

  = 3 ± 4i

Answer 2

Answer:

x= 3+4i , x= 3-4i

Step-by-step explanation:

x^2-6x= -25

To solve for x  we need to make right hand side

So add 25 on both sides

$x^2-6x+25=0$

Now apply quadratic formula

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

From the given equation a=1, b=-6  and c=25

Plug in all the values in the formula

$x=\frac{-(-6)+-\sqrt{(-6)^2-4(1)(25)}}{2(1)}$

$x=\frac{6+-\sqrt{-64}}{2}$

We know  $\sqrt{-1} =i$

So equation becomes

$x=\frac{6+8i}{2}$

Divide by 2

x= 3+-4i

So x= 3+4i , x= 3-4i