Question

Solve the following quadratic equation for x by completing the square and solve x^2-8x=-65​

Answer 1

Answer:

x= 4-7i  x= 4+ 7i

Step-by-step explanation:

step 1 : make equation = 0

$x^{2}$ - 8x + 65 = 0

step 2 : solve for x [ using the quadratic equation]

ie :     x = -b ± $\sqrt{b^{2}-4ac}$ / 2a

so it will look like this

x= -(-8) ± $\sqrt{(-8)^{2} - 4(1)(65)}$ /2(1)

when you simplify you wont be able to root the -196 so you will have to separate the roots

x = 8 ±( $\sqrt{-1}$ )( $\sqrt{196}$) / 2

now there is a rule for negative roots whereby  $\sqrt{-1}$ is equivalent to i so now you will change $\sqrt{-1}$ into i

Simplify $\sqrt{196}$

which will give you 14

now place all the new values into the formula

8 ± 14i /2

you can then further simplify to  

4 ± 7i

step 3 : separate

this will give you the final answer of

x= 4 + 7i   x= 4- 7i