mynameislol26 mynameislol26
  • 16-01-2020
  • Mathematics
contestada

5 times a number is 14 less than the square of that number. Find the negative solution.

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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 28-01-2020

Answer:

The negative solution is

[tex] - 2[/tex]

Step-by-step explanation:

Let the number be

Then 5 times the number is 5x.

14 less than the square of the number is

[tex] {x}^{2} - 14[/tex]

So our equation becomes

[tex]5x = {x}^{2}- 14[/tex]

This implies that

[tex]{x}^{2} - 5x - 14 = 0[/tex]

We factor to get:

[tex] {x}^{2} - 7x + 2x - 14 = 0[/tex]

[tex]x(x - 7) + 2(x - 7) = 0[/tex]

[tex](x - 7)(x + 2) = 0[/tex]

[tex]x + 7 = 0 \: or \: x - 2 = 0[/tex]

[tex]x = 7 \: or \: x = - 2[/tex]

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