Since <span><span>−11</span><span>-11</span></span> does not contain the variable to solve for, move it to the right side of the equation by adding <span>1111</span> to both sides.<span><span><span><span>x2</span>+<span>4x</span></span>=11</span><span><span><span>x2</span>+<span>4x</span></span>=11</span></span>To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of <span>bb</span>, the coefficient of <span>xx</span>.<span><span><span><span>(<span>b2</span>)</span>2</span>=<span><span>(2)</span>2</span></span><span><span><span>b2</span>2</span>=<span>22</span></span></span>Add the term to each side of the equation.<span><span><span><span><span>x2</span>+<span>4x</span></span>+<span><span>(2)</span>2</span></span>=<span>11+<span><span>(2)</span>2</span></span></span><span><span><span><span>x2</span>+<span>4x</span></span>+<span>22</span></span>=<span>11+<span>22</span></span></span></span>Simplify the equation.Tap for fewer steps...Simplify the right side.Tap for fewer steps...Simplify each term.Tap for more steps...<span><span><span><span><span>x2</span>+<span>4x</span></span>+<span><span>(2)</span>2</span></span>=<span>11+4</span></span><span><span><span><span>x2</span>+<span>4x</span></span>+<span>22</span></span>=<span>11+4</span></span></span>Add <span>1111</span> and <span>44</span> to get <span>1515</span>.<span><span><span><span><span>x2</span>+<span>4x</span></span>+<span><span>(2)</span>2</span></span>=15</span><span><span><span><span>x2</span>+<span>4x</span></span>+<span>22</span></span>=15</span></span>Simplify each term.Tap for fewer steps...Remove parentheses around <span>22</span>.<span><span><span><span><span>x2</span>+<span>4x</span></span>+<span>22</span></span>=15</span><span><span><span><span>x2</span>+<span>4x</span></span>+<span>22</span></span>=15</span></span>Raise <span>22</span> to the power of <span>22</span> to get <span>44</span>.<span><span><span><span><span>x2</span>+<span>4x</span></span>+4</span>=15</span><span><span><span><span>x2</span>+<span>4x</span></span>+4</span>=15</span></span>Factor the perfect trinomial square into <span><span><span>(<span>x+2</span>)</span>2</span><span><span>x+2</span>2</span></span>.<span><span><span><span>(<span>x+2</span>)</span>2</span>=15</span><span><span><span>x+2</span>2</span>=15</span></span>Solve the equation for <span>xx</span>.Tap for fewer steps...Take the square root of each side of the equation to setup the solution for <span>xx</span><span><span><span><span>(<span>x+2</span>)</span><span>2⋅<span>12</span></span></span>=<span>±<span>√15</span></span></span><span><span><span>x+2</span><span>2⋅<span>12</span></span></span>=<span>±15</span></span></span>Remove the perfect root factor <span><span>x+2</span><span>x+2</span></span> under the radical to solve for <span>xx</span>.<span><span><span>(<span>x+2</span>)</span>=<span>±<span>√15</span></span></span><span><span>x+2</span>=<span>±15</span></span></span>Remove parentheses.<span><span><span>x+2</span>=<span>±<span>√15</span></span></span><span><span>x+2</span>=<span>±15</span></span></span>Since <span>22</span> does not contain the variable to solve for, move it to the right side of the equation by subtracting <span>22</span> from both sides.<span>x=<span><span>−2</span>±<span>√<span>15
a) The measure of angle 7 is also 47 degrees. We know this because angle 5 and angle 7 are vertical angles and vertical angles are always equal.
b and c) Since we know that a straight line has an angle of 180 degrees and that the sum of angle 5 and angle 6 will add to this, we can use that to find the value of x like this:
