Complete the Square

Key Terms The process of adding a term to an expression 𝒙 𝟐 +𝒃𝒙 is called ___________________. Ex. 𝒂 𝒙 𝟐 +𝒃𝒙+ ?=𝒄

Example One Solve by finding the Square Root STEPS Write original equation. Write left side as a binomial squared. Take square roots of each side. Solve for x.

Example Two Solve by finding the Square Root Solve x2 – 10x + 25 = 1. STEPS Write original equation. Write left side as a binomial squared. Take square roots of each side. Solve for x.

You Try it!! Solve the equation by finding square roots. Solve x2 + 6x + 9 = 36.

Key Concept: Completing the Square To complete the square for expression 𝒙 𝟐 +𝒃𝒙 𝒂𝒅𝒅 𝒃 𝟐 𝟐

Example Three Making Perfect Square Trinomial Find the value of c then write as (ax + c)2 x2 + 14x + c STEPS STEP 1 Find half the coefficient of x. STEP 2 Square the result of Step 1. STEP 3 Replace c with the result of Step 2.

Example Four Find the value of c then write as (ax + c)2 x2 + 22x + c

You Try it!! Find the value of c, then write as a square binomial. x2 – 9x + c

Homework Textbook – Pg. 288 4,5,6, 13, 17,21 Write your Summary to the Essential Question