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            <h3>Solving Radical Equations</h3>
            <p>In this lesson, you will learn how to solve equations with radicals.</p>
            <p>Solving radical equations is a long process of simplifying, factoring, and testing with the given values of an equation. The standard steps of solving these equations are animated in the following video:</p>
            <video src="solving_equation.mp4" type="video/mp4" width="650" alt="Solving radical equation" controls></video>
            <p>Put into words, the steps are as follows:</p>
            <p>1. Simplify equation by isolating values of differing powers:</p>
            <span class="math">
                &radic;<span id="rad">x - 3</span> + 5 = x <br />
                &emsp; - 5 &emsp; &ensp; - 5 <br />
                &radic;<span id="rad">x - 3</span> = x - 5 <br />
                (&radic;<span id="rad">x - 3</span>)&sup2; = (x - 5)&sup2; <br />
                x - 3 = (x - 5)(x - 5)
            </span>
            <br />
            <p>2. Factor to simplify further:</p>
            <span class="math">
                x - 3 = (x - 5)(x - 5) <br />
                x - 3 = x&sup2; -5x - 5x +25 <br />
                x - 3 = x&sup2; -10x +25 <br />
                -x &emsp; &emsp; &ensp; -x <br />
                -3 = x&sup2; -11x +25 <br />
                +3 &emsp; &emsp; &emsp; &ensp; +3 <br />
                0 = x&sup2; -11x +28 <br />
                0 = (x - 7)(x - 4)
            </span>
            <br />
            <p>3. Elimanate extraneous solutions and find real solutions:</p>
            <span class="math">
                0 = (x - 7)(x - 4) <br />
                0 = x - 7 &emsp; 0 = x - 4 <br />
                +7 &ensp; +7 &emsp; +4 &ensp; +4 <br />
                7 = x &ensp; OR &ensp; 4 = x <br /><br />
                &radic;<span id="rad">(7) - 3</span> + 5 = (7) <br />
                &radic;<span id="rad">4</span> + 5 = 7 <br />
                2 + 5 = 7 <br />
                7 = 7 &ensp; &check;<br /><br />
                &radic;<span id="rad">(4) - 3</span> + 5 = (4) <br />
                &radic;<span id="rad">1</span> + 5 = 4 <br />
                1 + 5 = 4 <br />
                6 &ne; 4 &ensp; &cross;
            </span>
            <br />
            <p>4 is an <span class="tooltip">extraneous solution<span class="tooltiptext">A solution of the simplified form of an equation that does not satisfy the original equation and must be discarded</span></span> and is false; 7 is the true solution.</p>
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