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.

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.

... Given a quadratic equation: ax ² + bx + c Solve the equation for zero ... Four Steps to solve by factoring using the following example y=x2 + 2x + 1, note; a=1 ...

... of 18 Questions on Quadratic equations, factoring and solving word problems. Please see attached file for full problem description. 21.Factor completely : 6g ...

... the quadratic equation x2 - 3x + 2 = 0, perform the following tasks: Solve by factoring. ... The general form of the quadratic equation is ax^2+bx+c =0, Where a ...

... 2. Write the equation x(x - 7) + 10 = 0 in quadratic form and then solve it by factoring. ... 3. Solve the equation by using factoring. 3 x 3 - 192 x = 0. ...

... use the method of splitting the number (ab-c) into two factors whose sum ... This posting scrutinizes the factoring method of solving quadratic equations. ...

... Thus we have Four different methods of solving a quadratic equation have been discussed in this course: factoring, the square root property, completing ...

... Given a quadratic equation: ax² + bx + c Solve the equation for zero ... Four Steps to solve by factoring using the following example y=x² + 2x + 1, note; a=1 ...

... 2 22 4 Four different methods of solving a quadratic equation have been discussed in this course: factoring, the square root property, completing the ...