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Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
Polynomial Equations
Solving Linear Systems of Equations by Graphing
Quadratic Functions
Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Solving Linear Equations
Inequalities in one Variable
Recognizing Polynomial Equations from their Graphs
Scientific Notation
Factoring a Sum or Difference of Two Cubes
Solving Nonlinear Equations by Substitution
Solving Systems of Linear Inequalities
Arithmetics with Decimals
Finding the Equation of an Inverse Function
Plotting Points in the Coordinate Plane
The Product of the Roots of a Quadratic
Solving Quadratic Equations by Completing the Square
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Solving Quadratic Equations

by Completing the Square

Recall that x + 6 x + 9 is a trinomial square since ( x + 3 ) are its factors. Note that 3 is half of six.


Notes on Completing the Square

Completing the square is a procedure used to determine a solution of an equation by rewriting the equation as a trinomial square equal to a rational number.


Steps to solving quadratic equations by completing the square:

1. Isolate the variable terms on one side of the equation.

2. Divide both sides of the equation by the coefficient of   x . (This is not needed if the coefficient is 1.)

3. Determine the value needed to complete the square by dividing the coefficient of x by 2 and squaring the result.

4. Add the value obtained to both sides of the equation.

5. Rewrite the trinomial as a binomial square. 6. Use the principle of square roots to determine the possible solutions and solve.

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