Write a C++ program which will take in data from the user as a quadratic and solve the quadratic by Completing the Square. The steps to Completing the Square are as follows:

Applications of Completing the Square Method

Example 1: Solve the equation below using the method of completing the square.

Move the constant to the right side of the equation, while keeping the x-terms on the left. I can do that by subtracting both sides by 14.

Next, identify the coefficient of the linear term (just the x-term) which is

Take that number, divide by 2 and square it.

Add 81/4 to both sides of the equation, and then simplify.

Express the trinomial on the left side as a square of binomial.

Take the square roots of both sides of the equation to eliminate the power of 2 of the parenthesis. Make sure that you attach the plus or minus symbol to the constant term (right side of equation).

Solve for x by adding both sides by 9/2.

Find the two values of x by considering the two cases: positive and negative.

Therefore, the final answers are x1 = 7 and x2 = 2. You may back-substitute these two values of x from the original equation to check.

Example 2: Solve the equation below using the method of completing the square.

Solution:

Subtract 2 from both sides of the quadratic equation to eliminate the constant on the left side.

Divide 8 by 2 and square it.

Add 16 to both sides of the equation.

Express the left side as square of a binomial.

Take square roots of both sides.

Find the two values of x by considering the two cases: positive and negative.

Write a C++ program which will take in the value of a, b and c from the user and solve it by Completing the Square. Name your program CompleteSquare

Here are two sample outputs from the examples above:

and for the second example: