Chapter 9.6, Problem 33PPS

To determine

Solve the equation.

Answer to Problem 33PPS

Quadratic Formula $x=-0.8$ or $x=-6.2$

Explanation of Solution

Given Information: $x^2=-7x-5$

Formula Used: $D=b^2-4ac$ and $x=\frac{-b\pm \sqrt{D}}{2a}$

Calculation:

• $D$ equal to negative so $x$ has no real solution.
• $D$ equal to 0 so $x$ has 1 real solution.
• $D$ equal to positive so $x$ has 2 real solution.

  $x^2=-7x-5$

So, simplify

  $x^2+7x+5=0$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=1,b=7$ and $c=5$

  $D={\left(7\right)}^2-4\times 1\times 5$

Now,

  $D=49-20$

Hence,

  $D=29$

As, $D$ equal to positive so $x$ has 2 real solution.

  $x=\frac{-b\pm \sqrt{D}}{2a}$

So,

  $x=\frac{-7\pm \sqrt{29}}{2\times 1}$

Now, square root of 29 is 5.39.

  $x=\frac{-7\pm 5.39}{2}$

Now,

$x=\frac{-7+5.39}{2}$ or $x=\frac{-7-5.39}{2}$

Now,

$x=\frac{-1.61}{2}$ or $x=\frac{-12.39}{2}$

Hence,

$x=-0.8$ or $x=-6.2$