Question

Quadratic formula step by step

Answer 1

The final answer is the combination of both solutions x=5, -1

Explanation:

Solve using the Quadratic Formula: (-b+-√b^2-4ac) / 2a

-> Substitute the values a=1, b= -4, and c= -5 into the quadratic formula and solve for x.

-> Then, simplify.

Answer 2

Is that supposed to be x² -4x -5 = 0 or x²-4-5=0 as written? We'll do both.

As written it's

x²=9 so x=±3, no quadratic formula required.

Let's assume you meant

x² -4x - 5 = 0

So much temptation. This factors as

(x-5)(x+1)=0 so roots x=5, x=-1. But that didn't use the quadratic formula..

There's a shortcut to the quadratic formula called the Shakespeare Quadratic Formula (2b or -2b) that's useful when the linear term is even.

In that case x²-2bx+c has zeros at z=b±√(b²-c)

x = 2 ± √(4 - -5) = 2 ± √9 = 2 ± 3 = { -1 , 5 }

OK, let's do it like they want

x² - 4x - 5 = 0

We have a=1, b=-4, c=-5 and the quadratic formula

`x=(-b \pm √(b^2-4ac))/(2a)`

`x = (-(-4) \pm √((-4)^2-4(1)(-5)))/(2(1)) = \frac 1 2 (4 \pm √(36)) = \frac 1 2 (4 \pm 6) = \{-1, 5\}`

Answer: x=-1 or x=5