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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Quadratic Equations by Completing the Square

Now, we will complete the square to solve a quadratic equation.

 For example, letâ€™s solve: x2 + 2x = 4
We begin on the left-side of the equation by completing the square.
 To find the number needed to complete the square for x2 + 2x, calculate where b = 2. Thus, to complete the square for x2 + 2x, we add 1.
 However, we are working with an equation, so we must add 1 to both sides of the equation. x2 + 2x + 1 = 4 + 1 The left side can be written as the square of a binomial. (x + 1)2 = 5 To solve this equation, use the Square Root Property:  For each equation, subtract 1 from both sides.  So, the two solutions of x2 + 2x = 4 are We can write the solutions using shorthand notation: Here is a procedure we can use to solve any quadratic equation.

Note:

The symbol Â± is read â€œplus or minus.â€

Procedure â€” To Solve a Quadratic Equation by Completing the Square

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

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

Step 3 Find the number that completes the square:

â€¢ Multiply the coefficient of x by .

â€¢ Square the result.

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

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

Step 6 Finish solving using the Square Root Property.

Step 7 Check each solution.