Problem of the Week

Updated at Jun 17, 2024 3:09 PM

To get more practice in equation, we brought you this problem of the week:

How can we solve the equation \(2+{x}^{2}-\frac{4}{5}x=\frac{11}{5}\)?

Check out the solution below!



\[2+{x}^{2}-\frac{4}{5}x=\frac{11}{5}\]

1
Simplify  \(\frac{4}{5}x\)  to  \(\frac{4x}{5}\).
\[2+{x}^{2}-\frac{4x}{5}=\frac{11}{5}\]

2
Multiply both sides by \(5\).
\[10+5{x}^{2}-4x=11\]

3
Move all terms to one side.
\[10+5{x}^{2}-4x-11=0\]

4
Simplify  \(10+5{x}^{2}-4x-11\)  to  \(-1+5{x}^{2}-4x\).
\[-1+5{x}^{2}-4x=0\]

5
Split the second term in \(-1+5{x}^{2}-4x\) into two terms.
\[5{x}^{2}+x-5x-1=0\]

6
Factor out common terms in the first two terms, then in the last two terms.
\[x(5x+1)-(5x+1)=0\]

7
Factor out the common term \(5x+1\).
\[(5x+1)(x-1)=0\]

8
Solve for \(x\).
\[x=-\frac{1}{5},1\]

Done

Decimal Form: -0.2, 1
Cymath foriOSAndroid