Question 465533
Solve the quadratic equation x^2 - x = 30
:
x^2 - x + ___ = 30
Find the term that completes the square: half the coefficient of x, squared: (1/2)^2 = 1/4
Add to both sides
x^2 - x + {{{1/4}}}= 30 + {{{1/4}}}
x^2 - x + {{{1/4}}}= {{{120/4}}} + {{{1/4}}}
x^2 - x + {{{1/4}}}= {{{121/4}}}
Which is:
(x - {{{1/2}}})^2 = {{{121/4}}}
Find the square root of both sides
x - {{{1/2}}} = +/- {{{sqrt(121/4)}}}
x - {{{1/2}}} = +/- {{{11/2}}}
Two solutions
x = {{{1/2}}} + {{{11/2}}}
x = {{{12/2}}}
x = +6
and
x = {{{1/2}}} - {{{11/2}}}
x = {{{-10/2}}}
x = -5