Question

solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root properly.

x^2-10x+25=49

Answer 1

First off, let's factorize the left side of the equation, which is a perfect square trinomial.

x^2 - 10x + 25=49 can be factored as (x-5)^2=49.

Next step, we apply the square root property. Before we can apply the square root property, we need to isolate the perfect square trinomial on one side. The equation is already in this form.

Take the square root of both sides:
√((x-5)^2) = ±√49,

|x-5| = 7.

Since we are working with absolute values, there exist two possible solutions for x:

If it is positive:
x-5 = 7,
x = 7 + 5,
x = 12.

If it is negative:
x-5 = -7,
x = -7 + 5,
x = -2.

Therefore, the solutions to the equation are x = 12 and x = -2.