Equations and Inequalties: Tutorial 21 of 28 Save & Edt Question The square of a number,

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Equations and Inequalties: Tutorial

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The square of a number, x. is 16 less than eight times the number. What is the number?

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Hải Đăng 4 years 2021-08-09T16:56:24+00:00 1 Answers 11 views 0

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    2021-08-09T16:58:13+00:00

    Answer:

    The number is 4.

    Step-by-step explanation:

    We can answer the above question as follow:

    The square of a number, x is written as: x²

    Eight times the number is written as: 8x

    From the question, we were told that the square of the number, x is 16 less than eight times the number. This can be written as:

    x² = 8x – 16

    Rearrange

    x² – 8x + 16 = 0

    Solving by factorisation method:

    Multiply the 1st term (i.e x²) and the last term (i.e 16) together. The result is 16x² as shown below:

    x² × 16 = 16x².

    Next, find two factors of 16x² such that when we add them together, it will result to the 2nd term ( i.e – 8x).

    The factors are –4x and –4x.

    Next, replace – 8x in the equation with –4x and –4x. This is illustrated below:

    x² – 8x + 16 = 0

    x² – 4x – 4x + 16 = 0

    Factorise

    x(x – 4) – 4(x – 4) = 0

    (x – 4)(x – 4) = 0

    x – 4 = 0 or x – 4 = 0

    x = 4 or x = 4

    Thus, the number is 4.

    ***** Check *****

    x² = 8x – 16

    x = 4

    4² = 8(4) – 16

    16 = 32 – 16

    16 = 16

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