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Chapter 7: Q. 338 (page 893)

Solve Quadratic Equations by Factoring

In the following exercises, solve.

x+6x-3=-8

Short Answer

Expert verified

The solution isx=-5,2.

Step by step solution

01

Step 1. Given Information   

We are given the quadratic equation x+6x-3=-8 and we need to solve it by factoring.

02

Step 2. Solving the quadratic  

Multiplying the binomials:

x+6x-3=-8鈬�x2+6x-3x-18=-8鈬�x2+3x-18=-8

Writing the quadratic equation in standard form:

x2+3x-18=-8鈬�x2+3x-18+8=0鈬�x2+3x-10=0

Factoring the quadratic we get,

鈬�x2+5x-2x-10=0鈬�x(x+5)-2(x+5)=0鈬�(x+5)(x-2)=0

Use the Zero Product Property to set each factor to 0,

x+5=0鈬�x=-5x-2=0鈬�x=2

03

Step 3. Checking the answers   

Substituting each solution separately into the original equation:

x=-5,x+6x-3=-8鈬�-5+6-5-3=-8鈬�1脳-8=-8鈬�-8=-8x=2,x+6x-3=-8鈬�2+62-3=-8鈬�8脳-1=-8鈬�-8=-8

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Most popular questions from this chapter

Watermelon drop A springtime tradition at the University of California San Diego is the Watermelon Drop, where a watermelon is dropped from the seventh story of Urey Hall.

(a) The binomial -16t2+80 gives the height of the watermelon t seconds after it is dropped. Factor the greatest common factor from this binomial.

(b) If the watermelon is thrown down with initial velocity 8 feet per second, its height after t seconds is given by the trinomial-16t2-8t+80.Completely factor this trinomial.

Find the Greatest Common Factor from a polynomial

24pt4+16t7

Factor Differences of Squares

In the following exercises, factor.

49u3-9u

In the following exercises, find the greatest common factor.

42,60

Factor by grouping

ax鈭�ay+bx鈭�by
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