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+(7)/(6)x-(10)/(3)=0 \end{gathered}`

Completing the square,

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

To input the expression, we would have:

`(x+0.58)^2=3.67`

Solving for x,

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

To input this answer, we'll have:

x = -2.5 and x = 1.33