Question 570251
explain how to solve a quadratic equation by completing the square.
Using the example x^2 + 6x - 2 = 0
:
We complete the square by finding the third term, when we subtract 2 from both sides:
x^2 + 6x + ____ = 2
:
The third terms can be found by dividing the coefficient of x by 2 and squaring it.
In this case it is 6, half of 6 = 3, 3^2 = 9, so we add 9 to both sides
x^2 + 6x + 9 = 2 + 9
x^2 + 6x + 9 = 11
:
Factor to reveal a perfect square
(x+3)(x+3) = 11
or
(x+3)^2 = 11
:
Find the square root of both sides
x + 3 = +/-{{{sqrt(11)}}}
x = -3 +/-{{{sqrt(11)}}}
Two solutions
x = -3 + {{{sqrt(11)}}}
and
x = -3 - {{{sqrt(11)}}}