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If 18 is subtracted from twice the square of an integer, the
result is equal to nine times the integer. Find the integer.
[Only an algebraic solution will be accepted.]

Respuesta :

nasa231

Answer:

-3/2

Step-by-step explanation:

Let x = the integer:

2x^2 - 18 = 9x

2x^2 - 9x - 18 = 0

Now either factor that or use the quadratic formula if you're lazy like me.

x = -3/2 and 6, so x must be 6 because it has to be an integer.

akposevictor

Translating the statement into an algebraic equation, the integer found is: 6.

Recall:

  • Algebraic equations can be used in solving word problems to find unknown integers or numbers.
  • Integer is a whole number without a fractional part.

Thus, translate the statement given into an algebraic equation.

Let x = the unknown integer.

  • Therefore:

"18 subtracted from twice the square of an integer" is represented as 2x² - 18

"9 times the integer" is represented as 9x

The algebraic equation would be:

2x² - 18 = 9x

To solve for x, we need to factorize as shown below:

2x² - 18 = 9x

  • Subtract 9 x from both sides

2x² - 18 - 9x = 9x - 9x

2x² - 9x - 18 = 0

  • Factorize

(2x+3)(x−6)

2x = -3

x = -3/2

or

x - 6 = 0

x = 6

The integer therefore will be 6.

Learn more about algebraic equations here:

https://brainly.com/question/10612698

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