Using the quadratic formula, find the solution to 3x2 + 18x + 24 = 0.
(1 point)
• х = -4
02＝－2
02=4,2=2
• х = —2, х = —4
To find the solutions of the equation 3x^2 + 18x + 24 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = 18, and c = 24.
Substituting these values into the formula, we get:
x = (-18 ± √(18^2 - 4(3)(24))) / (2(3))
Simplifying further:
x = (-18 ± √(324 - 288)) / 6
x = (-18 ± √36) / 6
x = (-18 ± 6) / 6
This gives us two solutions:
x = (-18 + 6) / 6 = -12/6 = -2
x = (-18 - 6) / 6 = -24/6 = -4
So the solutions to the equation 3x^2 + 18x + 24 = 0 are x = -2 and x = -4.
To find the solutions to the quadratic equation 3x^2 + 18x + 24 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the values of a, b, and c in the equation ax^2 + bx + c = 0.
In this case, a = 3, b = 18, and c = 24.
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Step 3: Calculate the discriminant, which is the expression inside the square root:
Discriminant (D) = b^2 - 4ac
Step 4: Substitute the values of a, b, and c into the discriminant formula and calculate the discriminant:
D = (18^2) - 4(3)(24)
D = 324 - 288
D = 36
Step 5: Determine the solutions using the quadratic formula and the discriminant:
x = (-18 ± sqrt(36)) / (2 * 3)
Simplifying the expression inside the square root:
x = (-18 ± 6) / 6
Step 6: Calculate the solutions:
For the positive square root:
x1 = (-18 + 6) / 6
x1 = -12 / 6
x1 = -2
For the negative square root:
x2 = (-18 - 6) / 6
x2 = -24 / 6
x2 = -4
Therefore, the solutions to the quadratic equation 3x^2 + 18x + 24 = 0 are x = -2 and x = -4.
To find the solutions to the quadratic equation 3x^2 + 18x + 24 = 0 using the quadratic formula, follow these steps:
1. Identify the coefficients in the equation. In this case, the coefficient of the x^2 term is 3, the coefficient of the x term is 18, and the constant term is 24.
2. Substitute the values into the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a
Here, a = 3, b = 18, and c = 24.
3. Plug in the values into the quadratic formula:
x = (-18 ± √(18^2 - 4*3*24))/2*3
4. Simplify the equation inside the square root:
x = (-18 ± √(324 - 288))/6
x = (-18 ± √36)/6
x = (-18 ± 6)/6
5. Simplify further:
x = (-18 + 6)/6 or x = (-18 - 6)/6
x = -12/6 or x = -24/6
x = -2 or x = -4
So, the solutions to the equation 3x^2 + 18x + 24 = 0 are x = -2 and x = -4.