Solving Simple Quadratic Equations

Vocabulary and key concepts regarding the definition, solution count, and methods for solving simple quadratic equations.

Linear equations

Equations that have one solution.

Quadratic equation

An equation that has an $x^2$ in it.

Simple quadratic equation form

An equation of the form $x^2 = c$, where $c$ can be positive, zero, or negative.

Solutions for positive constant

If $c$ is positive, the equation $x^2 = c$ has two solutions.

Solutions for zero constant

If $c$ is zero, the equation $x^2 = c$ has one solution.

Solutions for negative constant

If $c$ is negative, the equation $x^2 = c$ has zero solutions.

Solving $x^2 = c$

To solve a simple quadratic equation, take the square root of both sides.

$\pm$ symbol

A symbol used to write one positive and one negative solution as a single statement as soon as you take the square root.

Surd

An exact answer that is left with a square root in it.

Decimal answer

An answer that is rounded off to a certain number of decimal places and is not exact.

Difference between $x = \sqrt{9}$ and $x^2 = 9$

The equation $x^2 = 9$ has two solutions ($3$ and $-3$), whereas $x = \sqrt{9}$ has only one solution ($3$).