Split - Quadratic equations

[cphilpott777]

my problem is (x - 1)^2=49 how do you get the exact solution

 

[Deleted member 4993]

my problem is (x - 1)^2=49 how do you get the exact solution

49 = 7[sup:ky3mvo71]2[/sup:ky3mvo71]

If

a[sup:ky3mvo71]2[/sup:ky3mvo71] - b[sup:ky3mvo71]2[/sup:ky3mvo71] = 0 , then

(a + b)(a - b) = 0 ? a + b = 0 ? a = -b

or

a - b = 0 ? a = b

so a = ± b

Follow the exact the same steps.

 

[mmm4444bot]

Another approach is to start by taking the square root of both sides.

You know that the square root of 49 is 7.

On the left-hand side, we have the square root of (x - 1)^2.

You need to know that the square root of an algebraic expression squared like (x - 1)^2 is the absolute value of the radicand.

In other words, the square-root of (x - 1)^2 is |x - 1|.

|x - 1| = 7

Now, follow the definition of absolute value, to get rid of the absolute value symbols. Then, finish by solving the two resulting equations in x.

 

[Deleted member 4993]

Let's do another problem

Solve for 'y' when:

(y + a)[sup:nsqb8d0l]2[/sup:nsqb8d0l] = b[sup:nsqb8d0l]2[/sup:nsqb8d0l]

(y + a)[sup:nsqb8d0l]2[/sup:nsqb8d0l] - b[sup:nsqb8d0l]2[/sup:nsqb8d0l] = 0

[(y + a) + b] [(y + a) - b] = 0

Then by applying 'zero product rule'

we have

[(y + a) + b] = 0

y = - a - b

or

[(y + a) - b] = 0

y = b - a

or we can write

y = -b ± a

put appropriate numbers and you are done!