# Solve the equation t^2+10=6t by completing square method?

Oct 27, 2016

$t = 3 - i$ or $t = 3 + i$

#### Explanation:

${t}^{2} + 10 = 6 t$ can be written as

${t}^{2} - 6 t + 10 = 0$

or ${t}^{2} - 6 t + 9 + 1 = 0$

Now we use the identity ${\left(x + 1\right)}^{2} = {x}^{2} + 2 x + 1$ and imaginary number $i$ defined by ${i}^{2} = - 1$

or ${t}^{2} - 2 \times 3 t + {3}^{2} - \left(- 1\right) = 0$

or ${\left(t - 3\right)}^{2} - {i}^{2} = 0$

Now using identity ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$, this becomes

$\left(t - 3 + i\right) \left(t - 3 - i\right) = 0$

Hence, either $t - 3 + i = 0$ i.e. $t = 3 - i$

or $t - 3 - i = 0$ i.e. $t = 3 + i$