Chapter 9.4, Problem 4CYU

To determine

Find the solutions.

Answer to Problem 4CYU

  $x=-0.16$ or $x=6.16$

Explanation of Solution

Given Information: ${(x-3)}^2=10$

Formula Used: $a^2-b^2=(a+b)(a-b)$

Calculation:

  ${(x-3)}^2=10$

So,

  ${(x-3)}^2-10=0$

As square root of 10 is $\sqrt{10}$ .

  ${(x-3)}^2-{\left(\sqrt{10}\right)}^2=0$

Now use formula, $a^2-b^2=(a+b)(a-b)$

  $(x-3+\sqrt{10})(x-3-\sqrt{10})=0$

So,

  $x=3-\sqrt{10}$ or $x=3+\sqrt{10}$

As, $\sqrt{10}=3.16$

  $x=3-3.16$ or $x=3+3.16$

Hence,

  $x=-0.16$ or $x=6.16$