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

Example

Solve using the Square Root Property: 16x2 - 24x + 9 = 81

Solution

 Step 1 Write the equation in the form x2 = a. The first and last terms of the trinomial are perfect squares. (4x)2 - 24x + (3)2 (4x)2 - 2(4x)(3)x + (3)2 = 81= 81 Since the trinomial has the form a2 - 2ab + b2, it is a perfect square trinomial. A perfect square trinomial can be written as the product of two identical binomials. (4x - 3)(4x - 3) (4x - 3)2 = 81= 81 Step 2 Use the Square Root Property.Step 3 Write each answer in simplified form. Simplify 81. To solve for x, add 3 to both sides. Divide both sides by 4. 4x - 3 = 9 or 4x = 12 or x = 3 or 4x - 3 = -94x = -6 Step 4 Check each answer. We leave the check to you.

So, the two solutions of 16x2 - 24x + 9 = 81 are 3 and

Note:

This equation can also be solved by factoring. We first write the equation in the form ax2 + bx + c = 0.

16x2 - 24x + 9 = 81

16x2 - 24x - 72 = 0

8(2x2 - 3x - 9) = 0

8(2x + 3)(x - 3) = 0

2x + 3 = 0 or x - 3 = 0