solve the following quadratic equqation using the quadratic formula
-2xd^2-7x+13=0
To solve the quadratic equation -2xd^2 - 7x + 13 = 0 using the quadratic formula, we need to identify the coefficients a, b, and c in the equation ax^2 + bx + c = 0.
In this case, the coefficients are:
a = -2
b = -7
c = 13
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
Substituting the values into the formula, we get:
x = ( -(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √(153)) / (-4)
Therefore, the solutions to the quadratic equation -2xd^2 - 7x + 13 = 0 are:
x = (7 + √153) / (-4)
x = (7 - √153) / (-4)
The quadratic equation you provided is: -2xd^2 - 7x + 13 = 0
To solve this equation using the quadratic formula, we can start by identifying the values of a, b, and c from the general form of a quadratic equation: ax^2 + bx + c = 0.
In this case:
a = -2d^2
b = -7
c = 13
Now, we can substitute these values into the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values we obtained earlier, we have:
x = (-(-7) ± √((-7)^2 - 4(-2d^2)(13))) / (2(-2d^2))
Simplifying this further:
x = (7 ± √(49 + 104d^2)) / (-4d^2)
Therefore, the solutions to the quadratic equation -2xd^2 - 7x + 13 = 0 are given by:
x = (7 + √(49 + 104d^2)) / (-4d^2)
x = (7 - √(49 + 104d^2)) / (-4d^2)
To solve the quadratic equation -2xd^2 - 7x + 13 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients and constant term
Here, the coefficients are:
a = -2
b = -7
c = 13
Step 2: Write down the quadratic formula
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
Step 3: Substitute the coefficients into the formula
Now, substitute the values for a, b, and c into the quadratic formula:
x = (-(-7) ± √((-7)² - 4*(-2)*13)) / (2*(-2))
Simplifying this equation further:
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √153) / (-4)
Step 4: Calculate the solutions
Using the ± sign, we calculate the two possible solutions for x:
x1 = (7 + √153) / (-4)
x2 = (7 - √153) / (-4)
So, the solutions to the quadratic equation -2xd^2 - 7x + 13 = 0, using the quadratic formula, are:
x1 = (7 + √153) / (-4)
x2 = (7 - √153) / (-4)