Chapter 9: Q.426. (page 983)

Solve by completing the square.
$(z - 10) (z + 2) = 28$

Short Answer

Expert verified

The required solution is $z = 12$ and $z = - 4$ .

Step by step solution

Step 1. Given information.

The given equation is $(z - 10) (z + 2) = 28$ .

Step 2. Find the equation by expanding the left-hand side of the equation.

$\begin{array}{rcl} (z - 10) (z + 2) & = & 28 \\ z (z + 2) - 10 (z + 2) & = & 28 \\ z^{2} + 2 z - 10 z - 20 & = & 28 \\ z^{2} - 8 z - 20 & = & 28 \end{array}$

Thus, the given equation is $z^{2} - 8 z - 20 = 28$ .

Step 3. Simplify the equation.

$\begin{array}{rcl} z^{2} - 8 z - 20 & = & 28 \\ z^{2} - 8 z - 20 + 20 & = & 28 + 20 \\ z^{2} - 8 z & = & 48 \\ z^{2} - 2 \cdot z \cdot 4 + 4^{2} & = & 48 + 4^{2} \dots \dots (a d d 16 o n b o t h s i d e s) \\ {(z - 4)}^{2} & = & 64 \\ z - 4 & = & \pm \sqrt{64} \\ z - 4 & = & \pm 8 \end{array}$

Step 4. Simplify the equation for z.

$\begin{array}{rcl} z - 4 & = & 8 \\ z & = & 8 + 4 \\ z & = & 12 \end{array}$ and $\begin{array}{rcl} z - 4 & = & - 8 \\ z & = & - 8 + 4 \\ z & = & - 4 \end{array}$

Step 5. Simplified answer.

Hence, the required solution is $z = 12$ and $z = - 4$ .

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Solve by completing the square.
$(z - 10) (z + 2) = 28$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation by expanding the left-hand side of the equation.

Step 3. Simplify the equation.

Step 4. Simplify the equation for z.

Step 5. Simplified answer.

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Solve by completing the square.z-10z+2=28

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation by expanding the left-hand side of the equation.

Step 3. Simplify the equation.

Step 4. Simplify the equation for z.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Geometry

Calculus

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$(z - 10) (z + 2) = 28$