(x-10)^2=20
Give exact and approximate solutions to three decimal places.
take √ of both sides ...
x-10 = ± √20
x = 10 ± √20 or 10 ± 2√5 <---- exact answer
I will let you push buttons on a calculator.
Thanks!
To solve the equation (x-10)^2 = 20, we can start by taking the square root of both sides of the equation. This will help eliminate the square term and allow us to isolate x.
√((x-10)^2) = √20
Now, we have two possibilities for the square root. One positive and one negative, since a squared term can result in either a positive or negative value when taking its square root.
x - 10 = ±√20
Next, we can solve for x by adding 10 to both sides of the equation:
x = 10 ± √20
The ± symbol represents both a positive and negative solution.
Now, let's calculate the exact and approximate solutions to three decimal places:
Exact solutions:
- For the positive solution: x = 10 + √20 ≈ 13.472
- For the negative solution: x = 10 - √20 ≈ 6.528
Approximate solutions to three decimal places:
- For the positive solution: x ≈ 13.472
- For the negative solution: x ≈ 6.528