Solve the following equation.
16x^2 − 16x + 4 = 0
x = 1 (smaller value)
x = 2 (larger value)
To solve the given equation 16x^2 − 16x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, the equation is 16x^2 − 16x + 4 = 0, so we can directly substitute the values of a, b, and c into the quadratic formula as follows:
x = (-(-16) ± √((-16)^2 - 4(16)(4))) / (2(16))
x = (16 ± √(256 - 256)) / 32
x = (16 ± √(0)) / 32
x = (16 ± 0) / 32
Here, we can see that the term under the square root, (256 - 256), is equal to 0. This means that taking the square root of 0 will give us 0, so the equation simplifies to:
x = (16 ± 0) / 32
Since the plus-minus sign indicates we have two possible solutions, we can calculate them separately:
Solution 1: (16 + 0) / 32 = 16 / 32 = 1/2 = 0.5
Solution 2: (16 - 0) / 32 = 16 / 32 = 1/2 = 0.5
Therefore, the solutions to the given equation are x = 0.5 or x = 1/2. However, in the provided solution, it seems like both x = 1 and x = 2 are stated as the solutions, which are not correct.
4 (4 x^2 - 4 x + 1) = 0
(2x-1)(2x-1) = 0
x = 1/2 or x = 1/2 (twice)
Now you do some.