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

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Answer 1 · 2015-03-30T18:23:00

This is the way:

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

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

$x - 7 = \pm 10 \Rightarrow x = 7 \pm 10 \Rightarrow$ $x-7=+-10rArrx=7+-10rArr$

$x_{1} = 7 - 10 = - 3$ $x_1=7-10=-3$

$x_{2} = 7 + 10 = 17$ $x_2=7+10=17$ .

How do you solve by completing the square: x2−14x=51x^2 - 14x = 51?