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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Quadratic Equations Using the Square Root Property

The Square Root Property can be used to solve a quadratic equation written in the form x2 = a.

Property â€” Square Root Property

If x2 = a, then

Here, a is a nonnegative real number.

Examples

If x2 = 7, then

If (w + 6)2 = 3, then

Hereâ€™s how to use the Square Root Property to solve a quadratic equation.

Procedure â€” To Solve a Quadratic Equation Using the Square Root Property

Step 1 Write the equation in the form x2 = a.

Step 2 Use the Square Root Property.

Step 3 Write each answer in simplified form.

Example 1

Solve using the Square Root Property: x2 - 72 = 0

Solution

 Step 1 Write the equation in the form x2 = a. Add 72 to both sides. x2 - 72x2 = 0= 0 Step 2 Use the Square Root Property. Step 3 Write each answer in simplified form.Simplify each square root. Step 4 Check each answer.

So, the equation x2 - 72 = 0 has two solutions, and -.

Example 2

Solve using the Square Root Property: -4x2 + 64 = 0

Solution

 Step 1 Write the equation in the form x2 = a. Subtract 64 from both sides. Divide both sides by -4. -4x2 + 64 -4x2 x2 = 0= -64 = 16 Step 2 Use the Square Root Property. Step 3 Write each answer in simplified form. Step 4 Check each answer. We leave the check to you. x = 4 or x = -4

So, the two solutions of -4x2 + 64 = 0 are 4 and -4.

Note:

Another way to write the solution is: