Question

Type the correct answer for each box write your answer in decimal form rounded to the nearest tenth if necessary type the solution with the smaller value in the first blank select and use the most direct method to solve 2x(x+1.5)=-1.

Answer 1

The solution is $x=-1$ and $x=-0.5$

Step-by-step explanation:

The expression is $2x(x+1.5)=-1$

Multiplying the term $x+1.5$ by $2x$, we get,

$2x^{2} +3x=-1$

Adding both sides by 1,

$2x^{2} +3x+1=0$

Taking factor, we get,

$\begin{array}{r}{x^{2}+2 x+x+1=0} \\{2 x(x+1)+1(x+1)=0} \\{(2 x+1)(x+1)=0}\end{array}$

Equating the factors to 0,

$\begin{aligned}2 x+1 &=0 \\2 x &=-1 \\x &=-\frac{1}{2}\\x&=-0.5\end{aligned}$ and $\begin{aligned}x+1 &=0 \\x &=-1\end{aligned}$

Thus, the smaller value is $x=-1$

The solution is $x=-1$ and $x=-0.5$