Learn on PengienVision, Algebra 1Chapter 9: Solving Quadratic Equations

Lesson 5: Completing the Square

In this Grade 11 enVision Algebra 1 lesson from Chapter 9, students learn how to use completing the square to solve quadratic equations, including cases where the leading coefficient is not 1. The lesson covers finding the value of (b/2)² to create a perfect-square trinomial, rewriting equations in binomial squared form, and applying the technique to real-world area problems. Students also use completing the square to convert quadratic functions into vertex form.

Section 1

Complete the Square of x^2 + bx

Property

To complete the square of $x^2 + bx$ :

Step 1. Identify $b$ , the coefficient of $x$ .

Step 2. Find $(\frac{1}{2}b)^2$ , the number to complete the square.

Section 2

Solve Equations by Completing the Square

Property

To solve a quadratic equation of the form $x^2 + bx + c = 0$ by completing the square:

Step 1. Isolate the variable terms on one side and the constant terms on the other.

Step 2. Find $(\frac{1}{2}b)^2$ , the number needed to complete the square. Add it to both sides of the equation.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Complete the Square of x^2 + bx

Property

To complete the square of $x^2 + bx$ :

Step 1. Identify $b$ , the coefficient of $x$ .

Step 2. Find $(\frac{1}{2}b)^2$ , the number to complete the square.

Section 2

Solve Equations by Completing the Square

Property

To solve a quadratic equation of the form $x^2 + bx + c = 0$ by completing the square:

Step 1. Isolate the variable terms on one side and the constant terms on the other.

Step 2. Find $(\frac{1}{2}b)^2$ , the number needed to complete the square. Add it to both sides of the equation.