Question

Solve for x -x2+3x+4=0

Answer 1

So for this, I will be factoring by grouping. Firstly, what two terms have a product of -4x² and a sum of 3x? That would be -x and 4x. Replace 3x with -x + 4x:

`-x^2-x+4x+4=0`

Next, factor -x² - x and 4x + 4 separately. Make sure that they have the same quantity inside of the parentheses:

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

Now you can rewrite the equation as
`(-x+4)(x+1)=0`

Now, apply the Zero Product Property to solve for x as such:

`-x+4=0\\-x=-4\\x=4\\\\x+1=0\\x=-1`

Your final answer is D. x = -1 and x = 4.

Answer 2

The correct answer is D) x = 4 and x = -1

In order to solve this, we plug into the quadratic equation.

x =
`\frac{-b +/- \sqrt{b^(2) - 4ac } }{2a}`

In this case, a is the coefficient of x^2 (-1), b is the coefficient of x (3) and c is the constant (4). Now we plug in and solve.

x =
`\frac{-(3) +/- \sqrt{3^(2) - 4(-1)(4) } }{2(-1)}`

x =
`(-3 +/- √(9 + 16 ) )/(-2)`

x =
`(-3 +/- √(25 ) )/(-2)`

x =
`\frac{-3 +/- 5 } }{-2}`

And then we'll split into the two possible answers.

(-3 + -5)/-2 = -8/-2 = 4

(-3 - -5)/-2 = 2/-2 = -1