Solve a Quadratic Congruence by Factors or Find the Square
This video discusses how to solve a system of quadratic congruences for the variable x which has no solutions for values of c in ax^2+bx+c=0 modulo 7
The question is 2x^2+3x+2=0 modulo 7.
First issue is that when finding the square, we need to make the b coefficient even, so we get an integer when dividing by 4.
Then we get the coefficient to correct the equation after finding the square needs to be multiplied by 2 as well and subtracting from the c value.
RHS needs to be a square value so when we take the square root, we have an integer. Take the square root on both sides to reveal a plus and minus value for the RHS. This reveals there is 1 solution.
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