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Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
Mixed
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Algebra
Order of Operations
Dividing Complex Numbers
Polynomials
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Factoring
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Numbers
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Fractions
Polynomials
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Exponents
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Radicals
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
   
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Solving Quadratic Equations

Strategies for Solving Quadratic Equations

You have learned four ways to solve a quadratic equation:

• The Square Root Property

• Factoring

• Completing the square

• The quadratic formula

You can solve any quadratic equation by completing the square or by using the quadratic formula. However, for some quadratic equations, it is quicker to solve by factoring or by using the Square Root Property.

When you want to solve a quadratic equation, try the following strategies:

1. Use the Square Root Property when the equation can be easily written in the form x2 = a or (x + k)2 = a.

For example, the Square Root Property is useful for solving this equation:

Add 16 to both sides.

 (x + 3)2 - 16 = 0

(x + 3)2 = 16

Use the Square Root Property to write two linear equations.
Simplify each square root.

Subtract 3 from both sides of each equation.

 x + 3 = 4 or x + 3 = -4

x =1 or x = -7

 

2. If the Square Root Property cannot be easily applied, write the equation in standard form, ax2 + bx + c = 0.

If the trinomial can be easily factored, solve the equation by factoring.

For example, this strategy is useful for solving this equation:

Add 6 to both sides of the equation.

Factor the trinomial.

Set each factor equal to 0.

Solve each equation.

 x2 - 5x = -6

x2 - 5x + 6 = 0

(x - 2)(x - 3) = 0

x - 2 = 0 or x - 3 = 0

x = 2 or x = 3

3. The quadratic formula can be used to solve any quadratic equation, including the equations in the two previous examples.
For example, the quadratic formula is useful for solving this equation:

 x2 + 1 = -5x

To write the equation in standard form, add 5x to both sides of the equation. x2 + 5x + 1 = 0
Use the quadratic formula with a = 1, b = 5, and c = 1.
Substitute the values for a, b, and c into the quadratic formula.
Simplify.
 
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