Question

Solve the quadratic equation by completing the square. If your answers are not an integer then type it as a decimal rounded to the nearest hundredth.6x^2+7x-20=0Completing the square gives us: (x+ Answer )^2 = AnswerEnter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.x=Answer and x=Answer

Answer 1

First, let's divide the equation by 6:

$\begin{gathered} 6x^2+7x-20=0 \\ \rightarrow x^2+\frac{7}{6}x-\frac{10}{3}=0 \end{gathered}$

Completing the square,

$\begin{gathered} x^2+\frac{7}{6}x-\frac{10}{3}=0 \\ \\ \rightarrow x^2+\frac{7}{6}x-\frac{10}{3}+\frac{529}{144}=\frac{529}{144} \\ \\ \rightarrow x^2+\frac{7}{6}x+\frac{49}{144}=\frac{529}{144} \\ \\ \rightarrow(x+\frac{7}{12})^2=\frac{529}{144} \end{gathered}$

To input the expression, we would have:

$(x+0.58)^2=3.67$

Solving for x,

$\begin{gathered} (x+\frac{7}{12})^2=\frac{529}{144} \\ \\ \rightarrow x+\frac{7}{12}=\pm\text{ }\sqrt[]{\frac{529}{144}} \\ \\ \rightarrow x=-\frac{7}{12}\pm\frac{23}{12} \\ \\ \rightarrow x_1=\frac{4}{3} \\ \rightarrow x_2=-\frac{5}{2} \end{gathered}$

To input this answer, we'll have:

x = -2.5 and x = 1.33