Question

how to solve x^2-6x+10

Answer 1

x^2-6x+10=0

Answer 2

Move everything to the left hand side.
Subtract 6 x from both sides:
\(x^2-6 x+10 = 0\)
Solve the quadratic equation by completing the square.
Subtract 10 from both sides:
\(x^2-6 x = -10\)
Take one half of the coefficient of x and square it, then add it to both sides.
Add 9 to both sides:
\(x^2-6 x+9 = -1\)
Factor the left hand side.
Write the left hand side as a square:
\((x-3)^2 = -1\)
Eliminate the exponent on the left hand side.
Take the square root of both sides:
\(x-3 = i\) or \(x-3 = -i\)
Look at the first equation: Solve for x.
Add 3 to both sides:
\(x = 3+i\) or \(x-3 = -i\)
Look at the second equation: Solve for x.
Add 3 to both sides...

Answer 3

Which leaves you with...?

Answer 4

x=3-i

Answer 5

could you show me how to do this using the quadratic formula, please?

Answer 6

I will give it a go :)

\[x=\frac{-6\pm\sqrt{6^2-4\times1\times10}}{2\times1}\]
\[x=\frac{-6\pm\sqrt{36-40}}{2}\]
\[x=\frac{-6\pm\sqrt{-4}}{2}\]
\[x=\frac{-6\pm\sqrt{4}\sqrt{-1}}{2}\]
\[x=\frac{-6\pm2i}{2}\]
\[x=\frac{-6+2i}{2} or \frac{-6-2i}{2}\]
\[x=\frac{2(-3+i)}{2} or \frac{2(-3-i)}{2}\]
\[x=i-3 \space or -3-i\]

Make sense?

Answer 7

this whole time I put A in the place of B. makes perfect sense now , thank you!(:

Answer 8

Haha, cool, nice work.