Question

When 5 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.

Answer 1

Answer:

x = -1

Step-by-step explanation:

First, we can translate this statement to the equation

$x^2-5=4x$

Subtracting 4x from both sides gives us a quadratic equation:

$x^2-4x-5=0$

From here, we can factor the expression on the right to give us the equation's two solutions. The factored form will look like

$(x+a)(x+b)=0$

We need a + b = -4 and ab = -5, and picking a = 1 and b = -5 do the job there. Our expression factors then to (x + 1)(x - 5), giving us the equation

$(x+1)(x-5)=0$

And the solutions x = -1 and x = 5. Since we're only looking for the negative solution, x = -1 is the one we want.