Algebra Tutorials!
Wednesday 17th of April
Calculations with Negative Numbers
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
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The Quadratic Formula

You can solve any quadratic equation by completing the square.

Now we will complete the square to solve ax2 + bx + c = 0. The solutions will be expressed in terms of a, b, and c. These solutions will give us a formula we can use to solve any quadratic equation.

Step 1 Isolate the x2-term and the x-term on one side of the equation.

Subtract c from both sides of the equation.

 ax2 + bx + c = 0

ax2 + bx = -c

Step 2 If the coefficient of x2 is not 1, divide both sides of the equation by the coefficient of x2.

The coefficient of x2 is a.

Divide both sides of the equation by a.
Step 3 Find the number that completes the square: Multiply the coefficient of x by . Square the result.

The coefficient of the x-term is .

Step 4 Add the result of Step 3 to both sides of the equation.

Add to both sides of the equation.

To combine like terms on the right side, write both fractions with denominator 4a2.

Combine like terms on the right side. In the numerator, write the b2-term first.

Step 5 Write the trinomial as the square of a binomial.

Step 6 Finish solving using the Square Root Property.

Use the Square Root Property. Rather than writing two separate equations, we write a single equation using the ± sign.
Subtract from both sides and simplify the radical.
Combine the fractions into a single fraction.


If a > 0, then 4a2 = 2a.

If a < 0, then 4a2 = -2a.


The result is called the quadratic formula.


Formula — The Quadratic Formula

The solutions of the quadratic equation ax2 + bx + c = 0 are given by the quadratic formula:

Here, a, b, and c are real numbers and a 0.

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