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# A number has the property that its square is equal to 84 more than five times the number. Enter all numbers that have this property.

+1
56
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+87

A number has the property that its square is equal to 84 more than five times the number. Enter all numbers that have this property.

May 3, 2020

#1
+300
+2

So we have a number $$x$$ that has this property that makes the following equation true:

$$x^2 = 84 + 5x$$

Changing this to standard quadratic form, we get:

$$x^2 - 5x - 84 = 0$$

This, factored into two binomials, is:

$$(x + 7)(x - 12) = 0$$

From this, $$x$$ must be either $$\fbox{-7 \text{ or 12}}$$. I guess those are your numbers :D

May 3, 2020

#1
+300
+2

So we have a number $$x$$ that has this property that makes the following equation true:

$$x^2 = 84 + 5x$$

Changing this to standard quadratic form, we get:

$$x^2 - 5x - 84 = 0$$

This, factored into two binomials, is:

$$(x + 7)(x - 12) = 0$$

From this, $$x$$ must be either $$\fbox{-7 \text{ or 12}}$$. I guess those are your numbers :D

CentsLord May 3, 2020
#2
+87
0

Thank you!

May 4, 2020