Solve the following quadratic equation using the perfect square trinomial pattern: 22
+ * + 0.25 = 0. (1 point)
О x = 0.25
O х = 0.5
О х = -0.25
О х = - 0.5
In order to solve the quadratic equation using the perfect square trinomial pattern, we need to rewrite the equation in the form of (a + b)^2 = 0.
Given the equation: x^2 + *x + 0.25 = 0
We can see that the first and third terms (x^2 and 0.25) are perfect squares: (x^2 = (x)^2 and 0.25 = (0.5)^2)
So, we can rewrite the equation as: (x + 0.5)^2 = 0
Now using the zero product property, we can set each factor equal to zero:
x + 0.5 = 0
Solving for x, we subtract 0.5 from both sides:
x = -0.5
Therefore, the solution to the quadratic equation is: x = -0.5.
To solve the quadratic equation using the perfect square trinomial pattern, we need to rewrite the equation in the form (x + a)^2 = 0.
Given equation: x^2 + 22x + 0.25 = 0.
In order to complete the perfect square trinomial, we need to add (b/2)^2 to both sides of the equation. Here, b = 22.
Adding (22/2)^2 = 11^2 = 121 to both sides, we get:
x^2 + 22x + 121 + 0.25 = 121
Simplifying the equation, we have:
(x + 11)^2 = 120.75
Now, to solve for x, we take the square root of both sides:
√((x + 11)^2) = √120.75
x + 11 = ±√120.75
x + 11 = ±√(3 * 40.25)
x + 11 = ±(±√3) * √40.25
x + 11 = ±(±√3) * 6.35
x + 11 = ± 6.35√3
To isolate x, we subtract 11 from both sides:
x = -11 ± 6.35√3
Therefore, the solutions to the quadratic equation x^2 + 22x + 0.25 = 0, using the perfect square trinomial pattern, are:
x = -11 + 6.35√3
x = -11 - 6.35√3
To solve the quadratic equation using the perfect square trinomial pattern, we need to rewrite the equation in the form (x + a)^2 = 0, where a is a constant.
The given equation, 22x^2 + *x + 0.25 = 0, is already in the form of a perfect square trinomial. The coefficient of the x^2 term is 22, which is a perfect square (4^2 = 16), and the constant term is 0.25, which is also a perfect square (0.5^2 = 0.25).
Therefore, we can rewrite the equation as:
(√22x + √0.25)^2 = 0
Now, we can take the square root of both sides of the equation to solve for x:
√((√22x + √0.25)^2) = ±√0
√22x + √0.25 = 0
Since the square root of any number is ± the square root of the positive value, we have:
√22x = -√0.25
Simplifying further:
√22x = -0.5
Now, to solve for x, we can square both sides of the equation:
(√22x)^2 = (-0.5)^2
22x = 0.25
Dividing both sides of the equation by 22:
x = 0.25 / 22
Simplifying further:
x = 0.01136363636...
So the solution to the quadratic equation is x = 0.0114 (rounded to 4 decimal places) or approximately x = 0.0114. Therefore, the correct answer is:
x = 0.0114 (± 0.0114)