sub_task_2_completing_the_square_.c

// Group Members
// David Henry - 1007604
// Rockell London - 1037481

#include <stdio.h>
#include <math.h>

// ax^2 + bx + c = 0

int a, b, c;
double newa, newb, newc, d, e, f, right_side, root1, root2;

int main()
{
	printf("COMPLETING THE SQUARE\n");
	//get the values
	printf("\nEnter A !=0 :");
	scanf("%d", &a);

	printf("\nEnter B:");
	scanf("%d", &b);

	printf("\nEnter C:");
	scanf("%d", &c);

	if (a == 1)
	{
		// when c is moved to rhs its polarity changes, we do this by *-1 since +*+=+, +*-=- ,-*-=+
		d = c *-1;

		// half of b squared
		e = pow(b / 2, 2);
		right_side = d + e;

		//half b
		f = b / 2;

		// + and - roots
		root1 = sqrt(right_side) - f;
		root2 = -sqrt(right_side) - f;

		// JUST PRINTING DOWN BELOW
		printf("\n(%d)x^2 + (%d)x + (%d) = 0\n\n", a, b, c);

		printf("Move constant to the RHS -->");
		printf("\n(%d)x^2 + (%d)x + __ = (%d)\n\n", a, b, c *-1);

		printf("Take half of b, square it, then add to both sides\n");
		printf("(%d)x^2 + (%d)x +  __  = (%0.2f)\n", a, b, d);
		printf("(%d)x^2 + (%d)x + (%0.2f) = (%0.2f) + (%0.2f)\n\n", a, b, e, d, e);

		printf("Rewrite the LHS as a perfect square\n");
		printf("((%dx + (%0.2f))^2 = (%0.2f)\n\n", a, f, (right_side));

		printf("Take the square root of both sides\n");
		printf("sqrt (((%dx + (%0.2f))^2) = sqrt (%0.2f)\n\n", a, f, (right_side));

		printf("Isolate and solve for X\n");
		printf("(%d)x + (%0.2f) = +- (%0.2f)\n\n", a, f, sqrt(right_side));
		printf("(%d)x = + (%0.2f) - (%.2f)\n\n", a, sqrt(right_side), f);
		printf("(%d)x = - (%0.2f) - (%.2f)\n\n", a, sqrt(right_side), f);

		printf("First root is: %0.2f\n\n", root1);
		printf("Second root is: %0.2f\n\n", root2);

	}
	else if (a > 1)
	{
		// since a is more than 1 we divide everything by a
		newa = (double) a / a;
		newb = (double) b / a;
		newc = (double) c / a;

		// when c is moved to rhs its polarity changes, we do this by *-1 since +*+=+, +*-=- ,-*-=+
		d = newc *-1;
		// half of b squared
		e = pow(newb / 2, 2);

		// calc rhs value 
		right_side = d + e;

		//half b
		f = newb / 2;

		// + and - roots
		root1 = sqrt(right_side) - f;
		root2 = -sqrt(right_side) - f;

		// JUST PRINTING DOWN BELOW
		printf("\n(%d)x^2 + (%d)x + (%d) = 0\n\n", a, b, c);

		printf("Move constant to the RHS -->");
		printf("\n(%d)x^2 + (%d)x + __ = (%d)\n\n", a, b, c *-1);

		printf("\nA != 1, so divide by A, %d", a);
		printf("\n(%d/a)x^2 + (%d/a)x + __ = (%d/a)\n\n", a, b, c *-1);

		printf("Take half of b, square it, then add to both sides\n");
		printf("(%0.0f)x^2 + (%0.2f)x +  __  = (%0.2f)\n", newa, newb, d);
		printf("(%0.0f)x^2 + (%0.2f)x + (%0.2f) = (%0.2f) + (%0.2f)\n\n", newa, newb, e, d, e);

		printf("Rewrite the LHS as a perfect square\n");
		printf("(((%0.0f)x + (%0.2f))^2 = (%0.2f)\n\n", newa, f, (right_side));

		printf("Take the square root of both sides\n");
		printf("sqrt (((%0.0fx + (%0.2f))^2) = sqrt(%0.2f)\n\n", newa, f, (right_side));

		printf("Isolate and solve for X\n");
		printf("(%0.0f)x + (%0.2f) = +- (%0.2f)\n\n", newa, f, sqrt(right_side));
		printf("(%0.0f)x = + (%0.2f) - (%.2f)\n\n", newa, sqrt(right_side), f);
		printf("(%0.0f)x = - (%0.2f) - (%.2f)\n\n", newa, sqrt(right_side), f);

		printf("First root is: %0.2f\n\n", root1);
		printf("Second root is: %0.2f\n\n", root2);

	}

	
	

	return 0;
}