The difference of the square of a number and 4 is equal to 3 times that number. Find the negative solution.

Question

The difference of the square of a number and 4 is equal to 3 times that number. Find the negative solution.

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Camila 2 weeks 2021-09-27T09:45:31+00:00 1 Answer 0

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    2021-09-27T09:46:45+00:00

    The negative solution is x = –1.

    Solution:

    Let the number be x.

    Square of a number = x²

    3 times a number = 3x

    Difference of square of a number and 4 = 3 times that number

    \Rightarrow x^2-4=3x

    Subtract 3x from both sides of the equation, we get

    \Rightarrow x^2-3x-4=0

    –3x can be written as x – 4x.

    \Rightarrow x^2+x-4x-4=0

    \Rightarrow( x^2+x)+(-4x-4)=0

    1st bracket have common term x and bracket have –4 common term.

    \Rightarrow x( x+1)-4(x+1)=0

    Take common term x + 1 outside.

    (x+1)(x-4)=0

    By zero factor principle, if AB = 0 then A = 0 or B = 0.

    x + 1 = 0,   x – 4 = 0

    x = –1,   x = 4

    The negative solution is x = –1.

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