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.