# How do you solve by completing the square: x^2 - 14x = 51?

Mar 30, 2015

This is the way:

${x}^{2} - 14 x = 51 \Rightarrow {x}^{2} - 14 x + {7}^{2} - {7}^{2} = 51 \Rightarrow$

${x}^{2} - 14 x + 49 = 51 + 49 \Rightarrow {\left(x - 7\right)}^{2} = 100 \Rightarrow$

$x - 7 = \pm 10 \Rightarrow x = 7 \pm 10 \Rightarrow$

${x}_{1} = 7 - 10 = - 3$

${x}_{2} = 7 + 10 = 17$.