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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.462. (page 984)

Solve the given equation.
$x + 7 x^{\frac{1}{2}} + 6 = 0$

Short Answer

Expert verified

There is no real solution.

Step by step solution

01

Step 1. Given information.

The given equation is $x + 7 x^{\frac{1}{2}} + 6 = 0$ .

02

Step 2. Simplify the equation.

$\begin{array}{rcl} x + 7 x^{\frac{1}{2}} + 6 & = & 0 \\ {(x^{\frac{1}{2}})}^{2} + 7 x^{\frac{1}{2}} + 6 & = & 0 \\ {(x^{\frac{1}{2}})}^{2} + 6 x^{\frac{1}{2}} + x^{\frac{1}{2}} + 6 & = & 0 \\ x^{\frac{1}{2}} (x^{\frac{1}{2}} + 6) + 1 (x^{\frac{1}{2}} + 6) & = & 0 \\ (x^{\frac{1}{2}} + 6) (x^{\frac{1}{2}} + 1) & = & 0 \end{array}$

03

Step 3. Solve the equation for x.

$x^{\frac{1}{2}} = - 1$ and $x^{\frac{1}{2}} = - 6$

The square of a number can't be negative.

Thus, the equation has no real solutions.

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