Using the quadratic formula, find the solution to 3x2+18x+24=0 .(1 point) Responses x=−2 x equals negative 2 x=−2 , x=−4 x equals negative 2 , x equals negative 4 x=−4 x equals negative 4 x=4 , x=2
To solve the quadratic equation 3x^2 + 18x + 24 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 3, b = 18, and c = 24. Plugging these values into the formula, we have:
x = (-18 ± √(18^2 - 4(3)(24))) / (2(3))
x = (-18 ± √(324 - 288)) / 6
x = (-18 ± √36) / 6
x = (-18 ± 6) / 6
Now we can simplify further:
x1 = (-18 + 6) / 6 = -12/6 = -2
x2 = (-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, we can follow these steps:
1. Identify the coefficients of the quadratic equation:
The coefficient of the quadratic term (x^2 term) is 3.
The coefficient of the linear term (x term) is 18.
The constant term is 24.
2. Write down the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
3. Substitute the coefficients into the quadratic formula:
In this case, a = 3, b = 18, and c = 24. Therefore, the quadratic formula becomes:
x = (-18 ± √(18^2 - 4 * 3 * 24)) / (2 * 3)
4. Simplify the expression inside the square root:
Calculate the discriminant, which is the expression inside the square root:
D = b^2 - 4ac
= 18^2 - 4 * 3 * 24
= 324 - 288
= 36
5. Determine the value of the square root:
Since the discriminant is positive (D > 0), we take the square root of 36, which is 6.
6. Apply the quadratic formula:
Substituting the values back into the quadratic formula, we have:
x = (-18 ± 6) / (2 * 3)
7. Simplify the expression inside the parentheses:
x = (-18 ± 6) / 6
8. Simplify the numerator:
x = (-12 ± 6) / 6
9. Simplify the expression:
x = (-12 + 6) / 6 = -6 / 6 = -1
x = (-12 - 6) / 6 = -18 / 6 = -3
Therefore, the solutions to the quadratic equation 3x^2 + 18x + 24 = 0 are x = -1 and x = -3.
To find the solutions using the quadratic formula, we can use the equation:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the equation is 3x^2 + 18x + 24 = 0.
Comparing this equation to the standard quadratic form ax^2 + bx + c = 0, we have:
a = 3, b = 18, c = 24.
Now, let's substitute these values into the quadratic formula:
x = (-18 ± √(18^2 - 4 * 3 * 24))/(2 * 3)
Simplifying further:
x = (-18 ± √(324 - 288))/(6)
x = (-18 ± √36)/(6)
x = (-18 ± 6)/(6)
Simplifying the expression:
x = (-18 + 6)/(6) or x = (-18 - 6)/(6)
x = -12/6 or x = -24/6
x = -2 or x = -4
Therefore, the solutions to the equation 3x^2 + 18x + 24 = 0 using the quadratic formula are:
x = -2 and x = -4.