[math]x^2-\frac{5}{2}x[/math]
[size=150]Noah is solving the equation [math]x^2+8x+15=3[/math]. He begins by rewriting the expression on the left in factored form and writes [math]\left(x+3\right)\left(x+5\right)=3[/math]. He does not know what to do next. [br][br]Noah knows that the solutions are [math]x=-2[/math] and [math]x=6[/math], but is not sure how to get to these values [/size][size=150]from his equation. [br][br]Solve the original equation by completing the square. [/size]
[size=150]An equation and its solutions are given. Explain or show how to solve the equation by completing the square.[/size][br][br][math]x^2+20x+50=14[/math]. The solutions are [math]x=-18[/math] and [math]x=-2[/math].
[math]x^2+1.6x=0.36[/math]. The solutions are [math]x=-1.8[/math] and [math]x=0.2[/math].
[math]x^2-5x=\frac{11}{4}[/math]. The solutions are [math]x=\frac{11}{2}[/math] and [math]x=-\frac{1}{2}[/math].
[math]x^2-0.5x=0.5[/math]
[math]x^2+0.8x=0.09[/math]
[math]x^2+\frac{13}{8}x=\frac{56}{36}[/math]
[size=150]Four students solved the equation [math]x^2+225=0[/math]. Their work is shown here. Only one student solved it correctly.[/size][br][br][table][tr][td]Student A:[/td][td]Student B:[/td][/tr][tr][td][math]\displaystyle \begin{align} x^2 +225&=0\\ x^2&=\text -225\\ x=15 \quad &\text{ or } \quad x= \text- 15\\ \end{align}\\[/math][br][/td][td][math]\displaystyle \begin{align} x^2 +225&=0\\ x^2&=\text -225\\ \text{No} &\text{ solutions} \end{align}\\[/math][br][/td][/tr][tr][td]Student C:[/td][td]Student D:[/td][/tr][tr][td][math]\displaystyle \begin{align} x^2 +225&=0\\ (x-15)(x+15)&=0\\ x=15 \quad \text{ or } \quad x&= \text- 15\\ \end{align}\\[/math][/td][td][math]\displaystyle \begin{align} x^2 +225&=0\\ x^2&=225\\ x=15 \quad &\text{ or } \quad x= \text- 15\\ \end{align}\\[/math][/td][/tr][/table][br]Determine which student solved the equation correctly. For each of the incorrect solutions, explain the mistake.[br]