Finding the Value that Completes the Square – Practice Problems

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Quadratic equations can be solved by using a certain method known as “completing the square”.

When solving quadratic equations by completing the square, first rewrite the function in standard form, ax² + bx + c = 0. If the value of a is greater than zero (a>0), then divide the whole equation by a such that the coefficient of x² is equal to one. The quadratic equation is now of the form x² + b/ax + c/a = 0.

Next, put the constant c/a on the right-hand side of the equation to get x² + b/ax = -c/a. To complete the square, write the left-hand side of the equation (x² + b/ax) as a perfect square trinomial by adding (b/2a)² to both sides of the equation, so that you have the expression x² + b/ax + (b/2a)² = -c/a+(b/2a)². To continue this process, factor and evaluate the equation.

Extract the square of the squared binomial by taking the square root of both sides of the equation; the result is a linear equation. Finally, solve the equation by simply isolating the variable x.

Notice that some quadratic equations have two solutions, some have one solution, and some even have two imaginary solutions.

Solve quadratic equations in one variable.

CCSS.MATH.CONTENT.HSA.REI.B.4.A

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Exercises in this Practice Problem
Explain how to solve the given function.
Solve the given quadratic equation.
Find the missing value $c$ that completes the square.
Decide which equation(s) will give General Good's jetpack the right distance to jump.
Identify the polynomial which is equal to $(a+b)^2$.
Find the two solutions of the following equation.