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Chapter 10: Q 10.40 (page 1174)

Solvez2+8z=-19.

Short Answer

Expert verified

The equation has no real solutions.

Step by step solution

01

Given Information  

The Given equation isz2+8z=-19.

02

Isolate the variable terms on one side and the constant terms on the other. 

The variable terms are on the left side.

z2+8z=-19

Here,b=8.

03

Find 12b2 and add to the both sides of equation.  

=12(8)2=42=16

Add 16both sides.

z2+8z+16=-19+16z2+8z+16=-3

04

Factor the perfect square trinomial as a binomial square.  

(z+4)2=-3

Use the square root property.

z+4=卤-3

Since -3is not a real number.

Thus, the equation has no real solutions.

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