Find the

Find the number x, which if it increases by 2, then its square increases by 21 percent.

Correct answer:

x =  20
y =  -0.9524

Step-by-step explanation:

$$\begin{gathered} q=21\mathrm{\%}=1+{\displaystyle \frac{21}{100}}=1.21 \\ (x+2{)}^2=x^2\ast q \\ (x+2{)}^2=x^2\cdot 1.21 \\ -0.21x^2+4x+4=0 \\ 0.21x^2-4x-4=0 \\ a=0.21;b=-4;c=-4 \\ D=b^2-4ac=4^2-4\cdot 0.21\cdot (-4)=19.36 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{4\pm \sqrt{19.36}}{0.42}} \\ {x}_{1,2}=9.52380952\pm 10.4761904762 \\ {x}_1=20 \\ {x}_2=-0.952380952381 \\ \text{ Factored form of the equation: } \\ 0.21(x-20)(x+0.952380952381)=0 \\ x=x_1=20 \end{gathered}$$

Our quadratic equation calculator calculates it.

$y=x_2=(-0.9524)=-{\displaystyle \frac{20}{21}}=-0.9524$

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