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Solving Quadratic Equations using Square Roots

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Solving Quadratic Equations using Square Roots

Study Guide

Key Definition

A quadratic equation in the form $a \, x^2 + b \, x + c = 0$ can be solved by square roots when $b = 0$.

Important Notes

When $b = 0$, the equation simplifies to $x^2 = d$.
Both positive and negative roots should be considered when solving.
This method is straightforward but only applicable when $b = 0$.
Always simplify the equation to isolate $x^2$.
Double-check your solutions by substituting back into the original equation.
If $d$ is negative, $√d$ is not a real number and the solutions are complex.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ represents multiplication

$\div$ represents division

$\sqrt{x}$ represents the square root of $x$

Remember to use proper notation when solving problems

Why It Works

By isolating $x^2$ and taking the square root, we directly solve for $x$ when $b = 0$, since the linear term is absent.

Remember

Always consider both $\pm \sqrt{d}$ as potential solutions for $x$.

Quick Reference

Standard Form:$a \, x^2 + c = 0$ → divide by $a$: $x^2 = -\frac{c}{a}$

Understanding Solving Quadratic Equations using Square Roots

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $x^2 = d$ leading to $x = \pm \sqrt{d}$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve $x^2 = 49$.

Real-World Problem

Question Exercise

Intermediate

Solve Quadratic Equation

Solve the quadratic equation $4 \, x^2 + 16 = 0$ for $x$ (where $x$ is a variable).

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given $9 \, x^2 = 81$, solve for $x$.

Challenge Quiz

Single Choice Quiz

Advanced

Solve the equation $16 \, x^2 = 64$.

Recap

Watch & Learn

Review key concepts and takeaways