A number is 90 less than its square. Find all such numbers.

Question

Solve the problem. Use the five-step problem-solving approach. A number is 90 less than its square. Find all such numbers.

Answer 1

I'm not sure what your teacher means by "5 step problem solving approach", but here's what I would do.

 

• Change your words into numbers.  A number (unknown, so use x) is 90 less than its square (x²)
• Make an equation for those words:  x=x²-90
• Rearrange and set to 0, so you can take advantage of factoring
• x²-x-90=0
• So to factor, we are looking for two numbers that multiply to -90, and add to -1.  Our only choices are -10 and 9
• (x+9)(x-10)=0
• Using the 0 property, either piece could be 0, so x could be -9 or 10