Use the quadratic formula to solve the equation.
-x^2+5x=3
a.5/2 +- sqrt13/2
b.-5/2 +- sqrt13/2
c.2/5 +- sqrt13/2
d.-2/5 +- sqrt13/2
same thing as
x^2 - 5x + 3 = 0
x = (5 ± √13)/2
which is the same as a)
To solve the equation -x^2 + 5x = 3 using the quadratic formula, we can start by rearranging the equation in the standard quadratic form: ax^2 + bx + c = 0.
In this case, a = -1, b = 5, and c = -3.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we have:
x = (-(5) ± sqrt((5)^2 - 4(-1)(-3))) / (2(-1))
Simplifying inside the square root:
x = (-5 ± sqrt(25 - 12)) / (-2)
x = (-5 ± sqrt(13)) / (-2)
Therefore, the correct answer is option b: -5/2 ± sqrt(13)/2.
To solve the equation -x^2 + 5x = 3 using the quadratic formula, we first need to rearrange the equation to the standard form ax^2 + bx + c = 0, where the coefficient of the x^2 term (a) is not negative.
Given equation: -x^2 + 5x = 3
Rearranging it: -x^2 + 5x - 3 = 0
Now, we can identify the values of a, b, and c:
a = -1
b = 5
c = -3
The quadratic formula is given by:
x = (-b +- sqrt(b^2 - 4ac)) / 2a
Plugging in the values from our equation, we have:
x = (-(5) +- sqrt((5)^2 - 4(-1)(-3))) / (2*(-1))
Simplifying this further:
x = (-5 +- sqrt(25 - 12)) / (-2)
x = (-5 +- sqrt(13)) / (-2)
Therefore, the correct answer is option d: -2/5 +- sqrt(13)/2.