times a number is 16 less than the square of that number. Find the negative solution.

Question

times a number is 16 less than the square of that number. Find the negative solution.

Answer 1

The statement of the problem does not give the multiple of x that is

"16 less than the square of that number [x]".

As an example, let the missing multiple of x be 6.

Six times a number is sixteen less than the square of that number.

6-----•----------x------ = ------(-16)------+--------------------x²-------------.

Rewrite as 6x = x² − 16 or x² − 6x − 16 = 0.

For x² − 6x − 16 = 0, use the quadratic equation formula for

Ax² + Bx +C = 0, which is x = {-B ± √[B² − 4AC]} ÷ 2A with:

A = 1;

B = -6;

C = -16.

Then obtain x = {-(-6) + √[(-6)² − (4×1×-16)]} ÷ (2×1) as 8.

Also obtain x = {-(-6) − √[(-6)² − (4×1×-16)]} ÷ (2×1) as -2.

Finally take the negative solution as x = -2.