# Solving Quadratic Equations With Factoring

Solving Quadratic Equations by Factoring is Chapter 13.7 page 955

1) Quadratic Equation is in STANDARD FORM (ax^2 + bx + c = 0 where a is positive)

Factor trinomial: x^2 + bx +c =(X + m)( X +n)=0 ,which :(mn=C),and (m+n=b)

(X + m)=0 ---->X = - m , and (X + n)=0----> X= - n

2) Pythagorean Theorem in Right triangle ( a^2 + b^2 = C^2),or( Leg^2 + Leg^2=Hypothenuse^2)

A. Solving Quadratic Equations With Factoring

1. Let's explore how consecutive integer problems work. We need to find two consecutive page numbers in a book such that the sum of the page numbers is 11 less than their product. How might we go about setting this problem up initially?

*******2. Your task is to anchor a ladder to the ground three feet from the wall of a house, and extend it up to a window that is 18 feet above the ground. Will a 20-foot ladder do the job? Begin by explaining which theorem you would use to set up the equation for this problem.

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#### Solution Preview

A. If n is the first page number, then n+1 is consecutive. We need to determine n so that the sum of these two consecutive numbers, n+(n+1), is eleven less than their product n(n+1). Thus, we need to find n such that

n+(n+1) = n(n+1)-11

...

#### Solution Summary

The expert examines solving quadratic equations with factors.