Chapter 9.5, Problem 5CYU

To determine

Find the solution.

Answer to Problem 5CYU

  $x=-1.16$ or $x=5.16$

Explanation of Solution

Given Information: $x^2+4x=6$

Formula Used: $a^2+2ab+b^2={(a+b)}^2$ and $a^2-b^2=(a+b)(a-b)$

Calculation:

  $x^2+4x=6$

So,

  $x^2+4x-6=0$

Now, adding & subtracting the square of half the coefficient of x.

  $x^2+4x-6+{\left(\frac{4}{2}\right)}^2-{\left(\frac{4}{2}\right)}^2=0$

Now use formula, $a^2+2ab+b^2={(a+b)}^2$

  ${\left(x+2\right)}^2-6-2^2=0$

So,

  ${\left(x+2\right)}^2-6-4=0$

So,

  ${\left(x+2\right)}^2-10=0$

Now, square root of 10 is $\sqrt{10}$

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

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

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

So,

  $x=-2-\sqrt{10}$ or $x=-2+\sqrt{10}$

Hence,

  $x=-1.16$ or $x=5.16$