Question 437377
Can you please solve the equation by completing the square: -10x = 3x² - 2
:
Re-write the equation in the form
3x^2 + 10x + ___ = 2
The coefficient of x^2 has to be 1, divide by 3, results:
x^2 + {{{10/3}}}x + ____ = {{{2/3}}}
:
Find the term which completes the square; (10/6)^2 = (100/36) reduces to {{{25/9}}}
x^2 + {{{10/3}}}x + {{{25/9}}} = {{{2/3}}} + {{{25/9}}}
:
x^2 + {{{10/3}}}x + {{{25/9}}} = {{{6/9}}} + {{{25/9}}}
:
x^2 + {{{10/3}}}x + {{{25/9}}} = {{{31/9}}}
:
(x + {{{5/3}}})^2 = {{{31/9}}}
:
x + {{{5/3}}} = +/-{{{sqrt(31/9)}}}
:
Two solutions
x = {{{-5/3}}} + {{{1/3}}}{{{sqrt(31)}}}
We can write it:
x = {{{(-5 + sqrt(31))/3}}}
and
x = {{{(-5 - sqrt(31))/3}}}