Question

(X+3)(X-8) = -30 solve using the quadratic formula

Answer 1

X = 3,2

Explanation:

1)Expand.

`x^(2)` - 8X+3X - 24 = -30

2)Simplify
`x^(2)`-8X+3X-24 to
`x^(2)`-5X - 24.

`x^(2)` – 5X – 24 = –30

3)Move all terms to one side.

`x^(2)` - 5X - 24+ 30 = 0

4)Simplify
`x^(2)`–5X-24+30 to
`x^(2)` - 5X + 6.

`x^(2)` - 5X + 6 = 0

5)Factor
`x^(2)`–5X+6.

(X-3)(X-2) = 0

6)Solve for X.

X = 3,2

Answer 2

To solve the equation (X+3)(X-8) = -30 using the quadratic formula, we first need to expand the left-hand side of the equation:

(X+3)(X-8) = X^2 - 5X - 24

Now we can rewrite the equation as:

X^2 - 5X - 24 = -30

Adding 30 to both sides, we get:

X^2 - 5X + 6 = 0

Now we can use the quadratic formula:

X = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -5, and c = 6.

Plugging these values into the formula, we get:

X = (-(-5) ± sqrt((-5)^2 - 4(1)(6))) / 2(1)
X = (5 ± sqrt(1)) / 2

Simplifying, we get:

X = 3 or X = 2

Therefore, the solutions to the equation (X+3)(X-8) = -30 are X = 3 and X = 2.