Answer:
5x = x^2 - 6
Step-by-step explanation:
<em>a number</em> can be represented by x,
<em>5</em><em> times a number</em> can be represented as the product of 5 and x, <em>6</em> <em>less than the square of that number</em> tells us that this is equal to a number squared minus 6. <em>is</em> tells us that these two expressions are equal.
If you want a working number, just solve by completing the square once this is in standard form. This is then converted to vertex form.
x^2-5x-6 = <u>(</u><u>x-5</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u><u>-</u><u>4</u><u>9</u><u>/</u><u>4</u> = (x^2-5x+25/4) -49/4 = x^2-5x-6.
(x-5/2)^2-49/4=0
(x-5/2)^2=49/4
(x-5/2) = ±√49/4
(x-5/2) = ±7/2
x=5/2±7/2
x=(5±7)/2
x=12/2,-2/2
x=6,-1
Thus, the number can either be 6 or -1.