Solve the following quadratic equation using the perfect square trinomial pattern: x2−16x+64 .(1 point) Responses x=−8 x equals negative 8 x=8 x equals 8 x=−64 x equals negative 64 x=64
To solve the quadratic equation x^2 - 16x + 64 using the perfect square trinomial pattern, we need to find the square root of the first and last term, and then combine them with the middle term.
The square root of the first term, x^2, is x.
The square root of the last term, 64, is 8.
Therefore, the pattern gives us (x - 8)^2.
Since the pattern is equal to the original equation, we have:
(x - 8)^2 = x^2 - 16x + 64.
We can solve this equation by using the square root property:
x - 8 = ±√(x^2 - 16x + 64).
Now, we will substitute the solutions inside the equation:
x - 8 = ±√(x^2 - 16x + 64)
x - 8 = ±√(x - 8)(x - 8)
x - 8 = ±(x - 8)
Now, we can solve for x:
x - 8 = x - 8 (taking the positive root)
x - x = 8 - 8
0 = 0
Since 0 = 0 is a true statement, it means that x can be any value.
Therefore, x can equal any real number.
Hence, the correct answer is x equals 8.
To solve the quadratic equation x^2 - 16x + 64 using the perfect square trinomial pattern, we need to rewrite the equation in the form (x - a)^2 = 0, where 'a' is a constant.
In this case, let's look at the equation x^2 - 16x + 64. We need to find two numbers that, when multiplied and doubled, will give us the middle term of -16x. In this case, -8 multiplied by -8 gives us 64, and -8 doubled gives us -16, which matches the middle term.
Therefore, we can rewrite the equation as (x - 8)^2 = 0.
To solve for x, we take the square root of both sides:
√((x - 8)^2) = √0
x - 8 = 0
Now, we isolate x:
x = 8
So the solution to the quadratic equation x^2 - 16x + 64 using the perfect square trinomial pattern is x = 8.
To solve the quadratic equation x^2 - 16x + 64 using the perfect square trinomial pattern, we can rearrange it as (x - 8)^2.
Now, we can set (x - 8)^2 = 0 and solve for x:
(x - 8)^2 = 0
Taking the square root of both sides:
x - 8 = 0
Adding 8 to both sides:
x = 8
Therefore, the solution to the quadratic equation x^2 - 16x + 64 is x = 8.