Question

X^2+3x−4=0 Solve for x. Write the smaller solution first, and the larger solution second.

smaller x=
larger x=

Answer 1

smaller x= -4

larger x= 1

Explanation:

x² + 3x - 4 = 0

x² + 4x - x - 4 = 0

x(x + 4) - (x + 4) = 0

(x - 1)(x + 4) = 0

x = -4, 1

Answer 2

smaller x: -4

larger x: 1

Explanation:

We need to factor this. In order to do so, we need to find factor pairs of the coefficient of x^2 (which is 1 in this case) and of the constant (-4 in this case) such that they add up to 3.

Here, the factors of 1 are obviously just 1 and 1. The factors of -4 are (1, -4), (-1, 4), and (2, -2). Notice that 1 * 4 + 1 * (-1) = 3, so we know that our factor pair from 1 is (1, 1) and our factor pair from -4 is (-1, 4).

Then, we factor this quadratic into: (x - 1)(x + 4) = 0. Now, solve for x by setting each of these two factors equal to 0:

x - 1 = 0 ⇒ x = 1

AND

x + 4 = 0 ⇒ x = -4

So, the solutions are x = -4 and x = 1.

Hope this helps!