Question 154135
Solve by "the method that came from India":
{{{x^2-2x-13 = 0}}}
Now I've never been to India, but the method to which you are refering is also known as "completing the square" and here's how you do that:
{{{x^2-2x-13 = 0}}} First, add 13 to both sides of the equation.
{{{x^2-2x = 13}}} Now "complete the square" in x by adding the square of half the x-coefficient to both sides of the equation. This would be: {{{(-2/2)^2 = 1}}}
{{{x^2-2x+1 = 13+1}}} Simplify.
{{{x^2-2x+1 = 14}}} Now factor the left side of the equation.
{{{(x-1)(x-1) = 14}}} Rewrite the left sides as:
{{{(x-1)^2 = 14}}} Now take the square root of both sides.
{{{x-1 = 0+-sqrt(14)}}} Finally, add 1 to both sides.
{{{highlight(x = 1+-sqrt(14))}}}