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+x2−45x=1152+{x}^{2}-\frac{4}{5}x=\frac{11}{5}?

Check out the solution below!



2+x2−45x=1152+{x}^{2}-\frac{4}{5}x=\frac{11}{5}

1
Simplify  45x\frac{4}{5}x  to  4x5\frac{4x}{5}.
2+x2−4x5=1152+{x}^{2}-\frac{4x}{5}=\frac{11}{5}

2
Multiply both sides by 55.
10+5x2−4x=1110+5{x}^{2}-4x=11

3
Move all terms to one side.
10+5x2−4x−11=010+5{x}^{2}-4x-11=0

4
Simplify  10+5x2−4x−1110+5{x}^{2}-4x-11  to  −1+5x2−4x-1+5{x}^{2}-4x.
−1+5x2−4x=0-1+5{x}^{2}-4x=0

5
Split the second term in −1+5x2−4x-1+5{x}^{2}-4x into two terms.
5x2+x−5x−1=05{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)=0x(5x+1)-(5x+1)=0

7
Factor out the common term 5x+15x+1.
(5x+1)(x−1)=0(5x+1)(x-1)=0

8
Solve for xx.
x=−15,1x=-\frac{1}{5},1

Done

Decimal Form: -0.2, 1
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