When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution.
Let the number be n.
Square of a number:
n^2
28 is subtracted from the square of a number:
n^2 - 28
3 times the number:
3n
The result is mean an equation, so we set n^2 - 28 = 3n
n^2 - 28 = 3n
Subtract 3n from each side:
n^2 - 3n - 28 = 3n - 3n
The right side cancels to 0, so we have:
n^2 - 3n - 28 = 0
This is a quadratic equation in standard form, so we use our quadratic calculator to solve:
We get two solutions for n:
n = (-4, 7)
The question asks for the negative solution, so our answer is:
n = -4
Let the number be n.
Square of a number:
n^2
28 is subtracted from the square of a number:
n^2 - 28
3 times the number:
3n
The result is mean an equation, so we set n^2 - 28 = 3n
n^2 - 28 = 3n
Subtract 3n from each side:
n^2 - 3n - 28 = 3n - 3n
The right side cancels to 0, so we have:
n^2 - 3n - 28 = 0
This is a quadratic equation in standard form, so we use our quadratic calculator to solve:
We get two solutions for n:
n = (-4, 7)
The question asks for the negative solution, so our answer is:
n = -4