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Completing the Square

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Completing the Square

Study Guide

Key Definition

Completing the square is a method used to solve a <a href="quadratic-equations">$ax^2 + bx + c = 0$</a> type quadratic equation. It involves transforming the equation into a perfect square.

Important Notes

The 'a' in the quadratic equation must not equal 0.
The roots of the equation are the values of x that satisfy the equation.
Completing the square involves adding the square of half the coefficient of the x-term to both sides of the equation.

Mathematical Notation

<a href="quadratic-equations">$ax^2 + bx + c$</a> represents a quadratic equation.

<a href="square-roots">$\sqrt{x}$</a> represents the square root of x.

Remember to use proper notation when solving problems.

Why It Works

Completing the square works because it transforms the quadratic equation into a format that can be easily solved by taking the square root of both sides.

Remember

Always remember to verify your solution by substituting the calculated roots back into the original equation.

Quick Reference

Quadratic Equation:<a href="quadratic-equations">$ax^2 + bx + c = 0$</a>

Understanding Completing the Square

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Completing the square is a method used to solve a quadratic equation by transforming it into a perfect square.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What does the 'a' in <a href="quadratic-equations">$ax^2 + bx + c = 0$</a> represent?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If a teenager throws a ball in the air with a velocity of 12 m/s, the height of the ball (h) can be calculated using the equation $h = -4.9t^2 + 12t$, where t is the time in seconds. Solve for t when h = 0 by completing the square.

Advanced Challenge

Thinking Exercise

Advanced

Think About This

Solve the equation $x^2 - 6x + 8 = 0$ by completing the square.

Recap

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Review key concepts and takeaways