This lesson from Openstax Intermediate Algebra 2E teaches students how to solve quadratic equations by completing the square, covering both the forms x² + bx + c = 0 and ax² + bx + c = 0. Students learn to recognize and apply the binomial squares pattern to transform expressions into perfect square trinomials, then apply the Square Root Property to find solutions. The technique builds on prior skills in factoring and expanding binomials and lays groundwork for later work with conic sections.
Section 1
📘 Solve Quadratic Equations by Completing the Square
Completing the square is a powerful method for solving any quadratic equation. By algebraically creating a perfect square trinomial, we can rewrite the equation to easily apply the Square Root Property and find the solutions.
This card is just the beginning. Next, you'll tackle interactive examples and practice problems to master completing the square for all types of quadratic equations.
Section 2
Complete a square of
To complete the square of :
Step 1. Identify , the coefficient of .
Step 2. Find , the number to complete the square.
Section 3
Solve by Completing the Square
To solve a quadratic equation of the form by completing the square:
Step 1. Isolate the variable terms on one side and the constant terms on the other.
Step 2. Find , the number needed to complete the square. Add it to both sides of the equation.
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Section 1
📘 Solve Quadratic Equations by Completing the Square
Completing the square is a powerful method for solving any quadratic equation. By algebraically creating a perfect square trinomial, we can rewrite the equation to easily apply the Square Root Property and find the solutions.
This card is just the beginning. Next, you'll tackle interactive examples and practice problems to master completing the square for all types of quadratic equations.
Section 2
Complete a square of
To complete the square of :
Step 1. Identify , the coefficient of .
Step 2. Find , the number to complete the square.
Section 3
Solve by Completing the Square
To solve a quadratic equation of the form by completing the square:
Step 1. Isolate the variable terms on one side and the constant terms on the other.
Step 2. Find , the number needed to complete the square. Add it to both sides of the equation.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter