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The square of a positive number decreased by 4 times the number is 12. Find the positive number. [Only an algebraic solution will be accepted.]

Respuesta :

sharonpatta
The math translation is: x^2-4x=12

So then you can subtract 12 from both sides and solve as a quadratic equation.

X^2-4x-12=0

This factors into:

(X-6)(x+2)=0.

So then the answer would be 6 or -2.
MrRoyal

When a number decreases, its value reduces.

The positive number is 6

Let the number be x.

So, the square of x is: x^2, and 4 times x is: 4x

The result is 12. So, we have:

[tex]\mathbf{x^2 - 4x = 12}[/tex]

Rewrite as:

[tex]\mathbf{x^2 - 4x - 12 = 0}[/tex]

Expand

[tex]\mathbf{x^2 - 6x + 2x - 12 = 0}[/tex]

Factorize

[tex]\mathbf{x(x - 6) + 2(x - 6) = 0}[/tex]

Factor out x - 6

[tex]\mathbf{(x + 2) (x - 6) = 0}[/tex]

Split

[tex]\mathbf{(x + 2) = 0\ or\ (x - 6) = 0}[/tex]

Solve for x

[tex]\mathbf{x = -2\ or\ x = 6}[/tex]

The number is positive.

So, we have:

[tex]\mathbf{x = 6}[/tex]

Hence, the positive number is 6

Read more about algebraic solution at:

https://brainly.com/question/14384499

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