Solve the following quadratic equation using the perfect square trinomial pattern: x ^ 2 + 10x + 25
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To solve the quadratic equation x^2 + 10x + 25 = 0 using the perfect square trinomial pattern, we need to recognize that it is in the form (x + a)^2 = 0.
By comparing it with the pattern, we can see that square of the first term is x^2, the square of the last term is 25, and twice the product of the first and second terms is 10x.
In this case, the first term is x, and the last term is 25. We need to find a value for "a" that, when squared, gives us 25. In this case, a = 5 since 5^2 = 25.
Thus, we can rewrite the equation as (x + 5)^2 = 0.
Now, to solve for x, we can take the square root of both sides, remembering that the square root of 0 is still 0:
√((x + 5)^2) = √0
(x + 5) = 0
x = -5
Therefore, the solution to the quadratic equation x^2 + 10x + 25 = 0 is x = -5.