Solve the following quadratic equation using the quadratic formula. −2x^2−7x+13=0 show all your work
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, a = -2, b = -7, and c = 13. Substituting these values into the quadratic formula, we have:
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 −2x^2−7x+13=0 are:
x = (7 + √153) / (-4)
x = (7 - √153) / (-4)
To solve the quadratic equation −2x^2−7x+13=0 using the quadratic formula, we start by identifying the coefficients of the equation:
a = -2
b = -7
c = 13
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the given coefficients, we have:
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √(153)) / (-4)
Now, let's simplify:
x = (7 ± √(9 * 17)) / (-4)
x = (7 ± 3√17) / -4
Therefore, the solutions to the quadratic equation −2x^2−7x+13=0 are:
x = (7 + 3√17) / -4
x = (7 - 3√17) / -4
To solve the quadratic equation −2x^2−7x+13=0 using the quadratic formula, we need to identify the coefficients a, b, and c, which represent the terms in the equation. In this case:
a = -2
b = -7
c = 13
Now, we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c, we have:
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
Simplifying:
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √153) / (-4)
Now, we have two possible solutions for x:
x1 = (7 + √153) / (-4)
x2 = (7 - √153) / (-4)
These are the solutions to the quadratic equation −2x^2−7x+13=0 when using the quadratic formula.