Question

When 21 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.

Answer 1

Answer:
x = - 3

Explanation:
Let, the number be 'x'.

Square of the number = x²
When 21 is subtracted from the square of a number = x² - 21
Result is 4 times the number =》x² - 21 = 4x

On solving,
x² - 21 = 4x
Change to a quadratic equation,
x² - 4x - 21 = 0
By splitting - the - middle - term,
x² - 7x + 3x - 21 = 0
x(x - 7) + 3 (x - 7) = 0
(x - 7)(x + 3) = 0

Negative solution:
(x + 3) = 0
=》x = - 3


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Hope it helps ⚜

Answer 2

Ok if I directly write the equation it will become difficult to understand , so I am dividing into small parts. :)

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Let :-

number be x.

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Part 1 :-

Statement :-

21 is subtracted from the square of a number.

x² ← square of number

Equation :-

x² - 21

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Part 2 :-

Statement :- the result is 4 times the number.

4 times a number means 4 × x = 4x.

Equation :-

x² - 21 = 4x

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Part 3 :-

So we got our equation i.e x² - 21 = 4x , now we can finally find negetive value of x.

→x² - 21 = 4x

→x² -21 - 4x = 0

→x² - 4x - 21 = 0

→x² + 3x - 7x - 21 = 0

→x(x + 3) - 7x - 21 = 0

→x(x+3) - 7(x + 3) = 0

→(x - 7) (x + 3) = 0

Comparing:-

• x - 7 = 0
• x = 7 ← possitive value

• x + 3 = 0
• x = - 3 ←negetive value

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Required answer :-

`\boxed{\pmb{\sf -3}}`