I need help with how to do these problems..

SOLVE THE EQUATION USING THE ZERO PRODUCT PROPERTY

-8n(5n+3)=0

SOLVE THE EQUATION BY COMPLETING THE SQUARE.. ROUND TO THE HEAREST HUNDRETHS

X^2-3x=4

4x^2+4x-24=0

Thank you... I don't get how to do these please explain. Thank you very much!

1.

-8n(5n+3)=0
set each factor equal to zero, then solve to get
n = 0 or n = -3/5

2.

x^2-3x=4
x^2 - 3x + 9/4 = 4 + 9/4
(x-3/2)^2 = 25/4

x-3/2 = ± 5/2
x = 4 or x = -1

3. divide each term by 4 to get

x^2 + x = 6
x^2 + x + 1/4 = 6 + 1/4
(x+1/2)^2 = 25/4
x + 1/2 = ±5/2
x = 2 or x = -3

Sure! I'd be happy to help. Let's start with the first problem:

SOLVE THE EQUATION USING THE ZERO PRODUCT PROPERTY:

-8n(5n + 3) = 0

To solve this equation using the Zero Product Property, we set each individual factor equal to zero and solve for n.

-8n = 0 or 5n + 3 = 0

Solving the first equation, we divide both sides by -8:

n = 0

For the second equation, we subtract 3 from both sides of the equation:

5n = -3

Then divide both sides by 5:

n = -3/5

Therefore, the solutions to the equation -8n(5n + 3) = 0 are n = 0 and n = -3/5.

Now, let's move on to the second problem:

SOLVE THE EQUATION BY COMPLETING THE SQUARE:

x^2 - 3x = 4

To solve this equation by completing the square, we follow these steps:

Step 1: Move the constant term to the other side of the equation:

x^2 - 3x - 4 = 0

Step 2: Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 - 3x + (3/2)^2 = 4 + (3/2)^2

This simplifies to:

x^2 - 3x + 9/4 = 4 + 9/4

Step 3: Simplify the equation:

(x - 3/2)^2 = 25/4

Step 4: Take the square root of both sides of the equation:

x - 3/2 = ±sqrt(25/4)

Simplifying further:

x - 3/2 = ± 5/2

Step 5: Solve for x by adding 3/2 to both sides of the equation:

x = 3/2 ± 5/2

This gives us two solutions: x = 8/2 and x = -2/2, which simplify to x = 4 and x = -1.

Therefore, the solutions to the equation x^2 - 3x = 4, rounded to the nearest hundredth, are x = 4 and x = -1.

Finally, let's move on to the third problem:

4x^2 + 4x - 24 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Comparing the given equation to the standard form ax^2 + bx + c = 0, we have:

a = 4, b = 4, c = -24

Substituting these values into the quadratic formula, we can solve for x:

x = (-4 ± sqrt(4^2 - 4(4)(-24))) / (2(4))

x = (-4 ± sqrt(16 + 384)) / 8

x = (-4 ± sqrt(400)) / 8

x = (-4 ± 20) / 8

Now, let's calculate the two possible solutions:

x = (-4 + 20) / 8 = 16 / 8 = 2

x = (-4 - 20) / 8 = -24 / 8 = -3

Therefore, the solutions to the equation 4x^2 + 4x - 24 = 0 are x = 2 and x = -3.

I hope that helps! Let me know if you have any further questions.