Solve the following quadratic equation using the quadratic formula. −2x2−7x+13=0 **Note: Make sure to enter both solutions together in the space provided using the ± symbol. For example: x={12±√10} (1 point) show all your work
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
In the given quadratic equation -2x² - 7x + 13 = 0, we have:
a = -2, b = -7, c = 13
Plugging these values into the quadratic formula:
x = (-(-7) ± √((-7)² - 4(-2)(13))) / (2(-2))
= (7 ± √(49 + 104)) / (-4)
= (7 ± √(153)) / (-4)
Therefore, the solution to the quadratic equation -2x² - 7x + 13 = 0 is:
x = (7 ± √(153)) / (-4)
x = (7 - √(153)) / (-4) and x = (7 + √(153)) / (-4)
To solve the quadratic equation −2x^2−7x+13=0 using the quadratic formula, we can first identify the coefficients of the quadratic equation:
a = -2
b = -7
c = 13
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
Now, substitute the values of a, b, and c into the quadratic formula:
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
Simplifying the formula:
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √(153)) / (-4)
Therefore, the two solutions to the quadratic equation are:
x = (7 + √(153)) / (-4)
x = (7 - √(153)) / (-4)
Hence, the solutions to the quadratic equation −2x^2−7x+13=0 using the quadratic formula are:
x = (7 + √(153)) / (-4)
x = (7 - √(153)) / (-4)
The quadratic equation is given as −2x^2−7x+13=0.
To solve this equation using the quadratic formula, we first need to identify the values of a, b, and c from the standard quadratic equation form (ax^2 + bx + c = 0).
In this case:
a = -2
b = -7
c = 13
Now, let's substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values:
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
= (7 ± √(49 + 104)) / (-4)
= (7 ± √153) / (-4)
Therefore, the solutions to the quadratic equation −2x^2−7x+13=0, using the quadratic formula, are:
x = (7 + √153) / -4, and x = (7 - √153) / -4
So, the final answer is:
x = (7 + √153) / -4, and x = (7 - √153) / -4