Answer:
6
Step-by-step explanation:
Let x by the unknown number.
Given:
- Eighty-five more than the square of a number is the same as the square of the quantity that is 17 less than the number.
Therefore, the equation representing the given information is:
[tex]\boxed{x^2+85=(x-17)^2}[/tex]
To solve for x, expand the right side:
[tex]\implies x^2+85=(x-17)^2[/tex]
[tex]\implies x^2+85=(x-17)(x-17)[/tex]
[tex]\implies x^2+85=x^2-34x+289[/tex]
Subtract x² from both sides of the equation:
[tex]\implies 85=-34x+289[/tex]
Add 34x to both sides:
[tex]\implies 34x+85=289[/tex]
Subtract 85 from both sides:
[tex]\implies 34x=204[/tex]
Divide both sides by 34:
[tex]\implies x=6[/tex]
Therefore the unknown number is 6.
