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

User PurTahan
by
9.1k points

2 Answers

2 votes
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


_________
Hope it helps ⚜

User Giho
by
7.9k points
10 votes

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


\\ \\

Let :-

number be x.


\\

Part 1 :-

Statement :-

21 is subtracted from the square of a number.

x² ← square of number

Equation :-

x² - 21


\\ \\

Part 2 :-

Statement :- the result is 4 times the number.

4 times a number means 4 × x = 4x.

Equation :-

x² - 21 = 4x


\\ \\

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


\\

Required answer :-


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

User Matt Hanley
by
8.7k points

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