Question

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$. $$ p^{2}-4 p+13=0 $$

Name: Problem 61, Chapter 8: Intermediate Algebra for College Students
Uploaded: 2020-07-03T00:18:18-08:00
Duration: 1 min 43 s
Channel: Julie Silva
Description: Solve each equation by completing the square. Write complex number solutions in the form a ±b i. p^2-4 p+13=0

   Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
p^{2}-4 p+13=0
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 8, Problem 61

Instant Answer

Solved by Expert Julie Silva

07/03/2020

Step 1

$$ p^2 - 4p = -13 $$ Show more…

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Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$. $$ p^{2}-4 p+13=0 $$

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Key Concepts

Completing the Square

Completing the square is a technique used to solve quadratic equations by rewriting the quadratic expression as a perfect square trinomial plus or minus a constant. This method involves rearranging the equation and adding the necessary constant term to both sides, which transforms the quadratic into a form that directly reveals the roots upon taking the square root of both sides.

Complex Numbers

Complex numbers are numbers that have both a real part and an imaginary part, expressed in the form a ± bi, where i is the imaginary unit such that i² = -1. They provide a way to express and work with the solutions of quadratic equations that have negative discriminants, meaning the equation does not have real solutions.

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