Solve the quadratic equation x2 + 6x − 7 = 0 using the completing the square method.

% MATLAB code to solve x^2 + 6x - 7 = 0 using the completing the square method

% Define coefficients of the quadratic equation ax^2 + bx + c = 0
a = 1;
b = 6;
c = -7;

% Step 1: Move the constant term to the right side and normalize by 'a'
% The equation becomes x^2 + (b/a)x = -c/a
% Since a=1 for this equation, it simplifies to x^2 + bx = -c
b_normalized = b / a; % Coefficient of x term after dividing by a
c_constant_on_right = -c / a; % Constant term on the right side after dividing by a

% Step 2: Calculate the term needed to complete the square
% This term is (b_normalized / 2)^2
term_to_add = (b_normalized / 2)^2;

% Step 3: Add the term to both sides
% The left side becomes (x + b_normalized/2)^2
% The right side becomes c_constant_on_right + term_to_add
right_side_value = c_constant_on_right + term_to_add;

% Step 4: Take the square root of both sides
% x + b_normalized/2 = +/- sqrt(right_side_value)
% Use 'complex' to handle cases where right_side_value might be negative (complex roots)
if right_side_value < 0
    sqrt_part = sqrt(complex(right_side_value));
else
    sqrt_part = sqrt(right_side_value);
end

% Step 5: Solve for x
x1 = -b_normalized / 2 + sqrt_part;
x2 = -b_normalized / 2 - sqrt_part;

% Display the solutions
fprintf('The quadratic equation is x^2 + 6x - 7 = 0.\n');
fprintf('Solutions using the completing the square method:\n');
fprintf('x1 = %f\n', x1);
fprintf('x2 = %f\n', x2);