Using the quadratic formula, find the solution to 3x^2+18x+24=0
To find the solution to the equation 3x^2+18x+24=0 using the quadratic formula, we first need to identify the coefficients a, b, and c in the general quadratic equation form: ax^2+bx+c=0.
In this case:
a = 3
b = 18
c = 24
The quadratic formula states that the solutions for x can be found using the formula:
x = (-b ± sqrt(b^2-4ac)) / 2a
Substituting the given values, we have:
x = (-18 ± sqrt((18)^2 - 4(3)(24))) / (2(3))
x = (-18 ± sqrt(324 - 288)) / 6
x = (-18 ± sqrt(36)) / 6
x = (-18 ± 6) / 6
This simplifies to two possible solutions:
x1 = (-18 + 6) / 6 = -12/6 = -2
x2 = (-18 - 6) / 6 = -24/6 = -4
Therefore, 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 first need to identify the values of the coefficients a, b, and c.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In our equation, we have:
a = 3
b = 18
c = 24
Now, we can substitute these values into the quadratic formula and calculate the solutions.
x = (-18 ± √(18^2 - 4 * 3 * 24)) / (2 * 3)
x = (-18 ± √(324 - 288)) / 6
x = (-18 ± √(36)) / 6
x = (-18 ± 6) / 6
Simplifying further:
For the positive root:
x = (-18 + 6) / 6
x = -12 / 6
x = -2
For the negative root:
x = (-18 - 6) / 6
x = -24 / 6
x = -4
Therefore, the solutions to the equation 3x^2 + 18x + 24 = 0 are x = -2 and x = -4.
To find the solutions of the quadratic equation 3x^2 + 18x + 24 = 0 using the quadratic formula, we can use the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a, b, and c represent the coefficients of the quadratic equation.
For the given quadratic equation 3x^2 + 18x + 24 = 0, we have:
a = 3
b = 18
c = 24
Now, let's solve the equation step by step:
Step 1: Identify the values of a, b, and c:
a = 3, b = 18, c = 24
Step 2: Calculate the discriminant (b^2 - 4ac):
Discriminant = (18^2) - (4 * 3 * 24) = 324 - 288 = 36
Step 3: Substitute the values into the quadratic formula:
x = (-18 ± √36) / (2 * 3)
Step 4: Simplify the expression inside the square root:
x = (-18 ± 6) / 6
Step 5: Simplify the expression:
x = (-18 + 6) / 6 or x = (-18 - 6) / 6
Step 6: Calculate the solutions:
x = (-12) / 6 or x = (-24) / 6
Step 7: Simplify the solutions:
x = -2 or x = -4
Therefore, the solutions to the quadratic equation 3x^2 + 18x + 24 = 0 are x = -2 and x = -4.