Final answer:
The negative solution to the equation x² - 3x - 4 = 0 is x = -1.
Step-by-step explanation:
The difference of the square of a number and 4 is equal to 3 times that number. To find the negative solution, let's represent the number as x.
The equation becomes x2 - 4 = 3x.
Rearranging the equation, we get x2 - 3x - 4 = 0.
To find the negative solution, we can use the quadratic formula: x = (-b - √(b2 - 4ac)) / (2a).
For our equation, a = 1, b = -3, and c = -4. Plugging these values into the quadratic formula, we get x = (-(-3) - √((-3)2 - 4(1)(-4))) / (2(1)).
Simplifying further, we get x = (3 - √(9 + 16)) / 2, which simplifies to x = (3 - √25) / 2.
The square root of 25 is 5, so x = (3 - 5) / 2, which equals -1.
Therefore, the negative solution to the equation is x = -1.