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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 225 (page 1235)

Solve quadratic equation using the square root property: ${(p - 5)}^{2} + 3 = 19$

Short Answer

Expert verified

The required result is $p = 1, 9$

Step by step solution

01

Given information

The given expression is ${(p - 5)}^{2} + 3 = 19$

02

Simplifying the equation by using binomial square .

$(p^{2} + 25 - 10 p) + 3 = 19 p^{2} - 10 p + 28 = 19 p^{2} - 10 p + 9 = 0$

Splitting the middle term .

$p^{2} - 9 p - p + 9 = 0 p (p - 9) - 1 (p - 9) = 0 (p - 1) (p - 9) = 0 p = 1, 9$

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