What are the solutions of the quadratic equation?
2x2 – 16x + 32 = 0
first divide by 2
x^2 - 8x + 16 = 0
I see a perfect square ...
(x-4)^2 = 0
x-4 = 0
x = 4
is this answer, right? ^^^^
reiny is still correct
Ah, the quadratic equation. Time to solve it with a little pizzazz! So, we have the equation 2x^2 - 16x + 32 = 0, huh? Well, let me tell you, solving this equation is like trying to find your missing sock in the dryer – a bit frustrating! But fear not, my friend, I'm here to make it fun.
To solve this quadratic equation, let's put on our mathematical clown shoes and use the legendary quadratic formula. Are you ready? Here it goes:
x = (-b ± √(b^2 - 4ac)) / (2a)
Now, let's identify the values for a, b, and c from our equation:
a = 2, b = -16, and c = 32.
Substitute those values into our formula and we get:
x = (-(-16) ± √((-16)^2 - 4(2)(32))) / (2(2))
Now, let's simplify that expression and calculate it:
x = (16 ± √(256 - 256)) / 4
x = (16 ± √0) / 4
Oh no! It seems like we've hit a clown-sized roadblock. The discriminant (the value inside the square root) is zero, which means there's only one solution to this quadratic equation. But don't be sad, my friend – one is better than none, right?
So, after all that clowning around, the solution to this equation is x = 4. Ta-da! That wasn't too bad, was it? Remember, math and humor go hand in hand, just like clown shoes!
To find the solutions of a quadratic equation, we can use the quadratic formula, which is a formula that allows us to find the values of x that satisfy the equation of the form ax^2 + bx + c = 0.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the equation 2x^2 - 16x + 32 = 0, we can identify a = 2, b = -16, and c = 32.
Now, we can substitute these values into the quadratic formula to find the solutions:
x = (-(-16) ± √((-16)^2 - 4(2)(32))) / (2(2))
x = (16 ± √(256 - 256)) / 4
x = (16 ± √0) / 4
Since the discriminant (√(b^2 - 4ac)) is zero, the two solutions coincide, resulting in one solution:
x = 16 / 4 = 4
Therefore, the quadratic equation 2x^2 - 16x + 32 = 0 has one solution, which is x = 4.