Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Solution
Given the expression below
Let the number be k
[tex]x^2-16x+k[/tex]To make it a perfect square, we apply the perfect square formula
[tex](x+a)^2[/tex]Equating both equations
[tex]\begin{gathered} x^2-16x+k=(x+a)^2 \\ x^2-16x+k=(x+a)(x+a) \\ x^2-16x+k=x(x+a)+a(x+a) \\ x^2-16x+k=x^2+ax+ax+a^2 \\ x^2-16x+k=x^2+2ax+a^2 \end{gathered}[/tex]Equating the terms
[tex]\begin{gathered} 2ax=-16x \\ \text{Divide both sides by 2x} \\ \frac{2ax}{2x}=\frac{-16x}{2x} \\ a=-8 \end{gathered}[/tex]Where the term added k is
[tex]\begin{gathered} k=a^2 \\ a=-8 \\ k=(-8)^2 \\ k=64 \end{gathered}[/tex]Substituting for k into the expression
[tex]\begin{gathered} x^2-16x+k \\ k=64 \\ x^2-16x+64 \end{gathered}[/tex]Hence, the trinomial is
[tex]x^2-16x+64[/tex]The number to be added is 64
Writing the trinomial as the square of a binomial becomes
[tex]\begin{gathered} x^2-16x+64 \\ =x^2-8x-8x+64 \\ =x(x-8)-8(x-8)_{} \\ =(x-8)(x-8) \\ =(x-8)^2 \end{gathered}[/tex]Hence, the square of the binomial is
[tex](x-8)^2[/tex]Thus, the number to be added is 64 and the square of the binomial is (x - 8)²
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
