Lucky number

Philip multiplied the number 4 twice in a row by his lucky number. He added 4 to the result and got a result of 200. What is Philip's lucky number?

Final Answer:

x₁ =  7
x₂ =  -7

Step-by-step explanation:

$$\begin{gathered} 4\cdot x\cdot x+4=200 \\ 4\cdot x\cdot x+4=200 \\ 4x^2-196=0 \\ 4=2^2 \\ 0 \\ 196=2^2\cdot 7^2 \\ \text{GCD}(4,0,196)=2^2=4 \\ {x}^2-49=0 \\ {x}_{1,2}=\pm \sqrt{49}=\pm 7 \\ {x}_1=7 \\ {x}_2=-7 \\ {x}_1=7 \end{gathered}$$

Our quadratic equation calculator calculates it.

$x_2=(-7)=-7$

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