Question

Solve the equation, give the exact solution then approximate the solution to the nearest hundredth

Answer 1

Given the expression:

`10-3x^2=4`

We can find its solution by solving like a linear equation up until the exponent:

`\begin{gathered} 10-3x^2=4 \\ \Rightarrow-3x^2=4-10 \\ \Rightarrow-3x^2=-6 \\ \Rightarrow x^2=(-6)/(-3)=2 \\ x^2=2 \end{gathered}`

now, we can apply the square root on both sides to get the following:

`\begin{gathered} \sqrt[]{x^2}=\sqrt[]{2} \\ \Rightarrow x=\pm\sqrt[]{2=} \\ x=\pm1.41 \end{gathered}`

therefore, the solutions of the equation are x=1.41 and x=-1.41