solve 2x^2 = 9x. round to the nearest tenth.
a)x = 0 or x = -4.5
b)x = 4.5
c)x = 1.5 or x = 3
d)x = 0 or x = 4.5
i think the answer is d but i could be wrong
2x^2 = 9x
2 x^2 - 9 x = 0
x (2x-9) = 0
x = 0
or
x = 4.5
To solve the equation 2x^2 = 9x, we will begin by rearranging the equation into quadratic form, bringing all the terms to one side:
2x^2 - 9x = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 2, b = -9, and c = 0.
Next, we can apply the quadratic formula, which states that for any quadratic equation ax^2 + bx + c = 0:
x = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values from our equation:
x = (-(-9) ± √((-9)^2 - 4(2)(0)))/(2(2))
Simplifying:
x = (9 ± √(81))/(4)
x = (9 ± 9)/(4)
Now, we can solve for the two possible values of x:
x1 = (9 + 9)/4 = 18/4 = 4.5
x2 = (9 - 9)/4 = 0
So, the correct answer is option D: x = 0 or x = 4.5.