<h2><u>
Answer:</u></h2><h2><u />
![\boxed{4x^2-15x-4=(x-4)(4x+1)}](https://tex.z-dn.net/?f=%5Cboxed%7B4x%5E2-15x-4%3D%28x-4%29%284x%2B1%29%7D)
<u /></h2><h2><u /></h2><h2>
<u>Solution Steps:</u></h2>
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<h3>
</h3><h3>
1.) <u>
Change the equation using factored transformation:</u>
</h3>
<em> - Quadratic polynomial can be factored using the transformation </em>
<em>, where </em>
<em> and </em>
<em> are the solutions of the quadratic equation </em>
<em>. </em>
<em> - This steps basically means change you current equation using the formula </em>
<em>. </em>
<h3>2.) <u>Turn the factored form into the quadratic equation form:</u></h3>
<em> - All equations of the form </em>
<em> can be solved using the quadratic formula: </em>
<em>.</em>
<em> - The quadratic equation formula gives two solutions, one when </em>
<em> is addition and one when it is subtraction. </em>
<em />
<h3>3.) <u>Square -15:</u></h3>
<u>Equation at the end of Step 3:</u>
- <u />
<u />
<u />
<h3>4.) <u>Multiply −4 times 4:</u></h3>
× ![4=-16](https://tex.z-dn.net/?f=4%3D-16)
<u>Equation at the end of Step 4:</u>
- <u />
<u />
<h3 /><h3>5.) <u>Multiply −16 times −4:</u></h3>
× ![-4=64](https://tex.z-dn.net/?f=-4%3D64)
<u>Equation at the end of Step 5:</u>
- <u />
![x=\frac{-(-15)\frac{+}{}\sqrt{225+64}}{2\bold{x}4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-15%29%5Cfrac%7B%2B%7D%7B%7D%5Csqrt%7B225%2B64%7D%7D%7B2%5Cbold%7Bx%7D4%7D)
<h3 /><h3>6.) <u>Add 225 to 64:</u></h3>
<u>Equation at the end of Step 6:</u>
- <u />
<u />
<h3 /><h3>7.) <u>Take the square root of 289:</u></h3>
<u>Equation at the end of Step 7:</u>
- <u />
<u />
<h3 /><h3>8.) <u>Change -15 to positive 15:</u></h3>
<u>Equation at the end of Step 8:</u>
- <u />
<u />
<h3 /><h3>9.) <u>Multiply 2 by 4:</u></h3>
× ![4=8](https://tex.z-dn.net/?f=4%3D8)
<u>Equation at the end of Step 9:</u>
- <u />
<u />
<h3> </h3><h3>10.) <u>Now Solve:</u></h3>
<em>Now solve the equation </em>
<em> when </em>
<em> is plus.</em>
<em>Add 15 to 17:</em>
- <em />
<em />
- <em />
<em><u /></em>
<em>Divide 32 by 8: </em>
÷ ![8=4](https://tex.z-dn.net/?f=8%3D4)
<em>Now solve the equation </em>
<em> when </em>
<em> is minus.</em>
<em>Subtract 15 by 17:</em>
<em> Reduce the fraction to lowest terms by extracting and canceling out 2:</em>
÷
÷ ![-2=-4](https://tex.z-dn.net/?f=-2%3D-4)
<h3>11.) <u>Factor the expression:</u></h3>
<em>Factor the original expression using </em>
<em>. Substitute 4 for </em>
<em> and </em>
<em> for </em>
<em>:</em>
- <em />
<em />
<em />
<em>Simplify all the expressions of the form </em>
to
<em>:</em>
<em>Add </em>
<em> to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible:</em>
<em>Cancel out 4, the greatest common factor in 4 and 4:</em>
- <em />
<em />
<em />
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