Question

Select the two values of x that are roots of 7x-15= -2x².

Answer 1

Solution

- The solution steps are given below:

$\begin{gathered} 7x-15=-2x² \\ \text{ Add }2x^2\text{ to both sides} \\ \\ 2x^2+7x-15=0 \\ \\ \text{ The x-term can be rewritten as:} \\ 7x=10x-3x \\ \\ \text{ Thus, we have:} \\ 2x^2+10x-3x-15=0 \\ \text{ Factorize,} \\ 2x(x+5)-3(x+5)=0 \\ (x+5)\text{ is common, thus, we can factorize again.} \\ \\ (x+5)(2x-3)=0 \\ \\ \text{ This implies that} \\ \\ (x+5)=0\text{ or }(2x-3)=0 \\ \text{ Solving for x, we have:} \\ \\ x=-5\text{ or }x=\frac{3}{2} \end{gathered}$

Final Answer

$\begin{gathered} x=-5\text{ \lparen OPTION A\rparen} \\ \\ x=\frac{3}{2}\text{ \lparen OPTION C\rparen} \end{gathered}$