4. Find the solutions of each of the following QE by factoring. Explain how you arrived at your answer.

a. (x+3)^2 = 25 c. (2t - 3)^2 = 2t^2 + 5t - 26

b. (s+4)^2 = -2s d. 3(x+2)^2 = 2x^2 + 3x - 8

5. Do you agree that x^2 + 5x - 14 = 0 and 14 - 5x - x^2 = 0 have the same solutions? Justify your answer.
6. Show that the equation (x - 4)^2 = 9 can be solved both by factoring and extracting square roots.

7. A computer manufacturing company would like to come up with a new
laptop computer such that its monitor is 80 sq inches smaller than the
present ones. Suppose the length of the monitor of the larger computer
is 5 inches longer than its width and the area of the smaller computer
is 70 sq inches. What are the dimensions of the monitor of the larger
computer?

THANK YOU PO :)

2

Answers

2014-06-29T16:44:51+08:00
(x-3)^2 = 25
x^2 + 9 - 6x = 25
x^2 - 6x + 9 - 25 = 0
x^2 - 6x - 16 = 0
x^2 - 8x + 2x - 16 = 0
x(x - 8) + 2(x - 8) = 0
(x + 2)(x - 8) = 0
x = -2 , 8


1 5 1
lleter a
Ah. OK
WHAT IS THE ANSWER OF (A6
WHAT I MEAN IS (A^2 B^2 + 8C^4
Eh? bakit ganun?? ang nakalagay sa sa testpaper namin a. (x + 2)^2 = 9 tapos yung sa no. 6 (x - 2)^2 = 9? kaya hindi ko alam yung sagot. HUHUHU!!! help!
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2014-06-29T17:51:45+08:00

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4. (x+3)^2=25
 \sqrt{(x+3)^2}= + or-\sqrt{25}
x+3=+or-5
x=5-3
x=2
x=-5-3
x=-8
 \left \{ {{x=2} \atop {x=-8}} \right.

(s+4)^2=-2s
s^2+8s+16+2s=0
s^2+10s+16=0
s^2+10s=-16
s^2+10s+(5)^2=-16+(5)^2
 \sqrt{(s+5)^2}=+or- \sqrt{9}
s+5=+or-3
s=3-5
s=-2
s=-3-5
s=-8
 \left \{ {{x=-2} \atop {x=-8}} \right.

(2t-3)^2=2t^2+5t-26
4t^2-12t+9=2t^2+5t-26
4t^2-2t^2-12t-5t+9+26=0
2t^2-17t+35=0
2t^2-17t=-35
 \frac{2t^2-17t}{2} = \frac{-35}{2}
t^2- \frac{17}{2}t=- \frac{35}{2}
t^2- \frac{17}{2} t+( \frac{17}{4})^2=- \frac{35}{2}+( \frac{17}{4})^2
 \sqrt{(t- \frac{17}{4}) } =+or-  \sqrt{ \frac{289}{16} }
t- \frac{17}{4}=+or- \frac{17}{4}
t= \frac{17}{4}+ \frac{17}{4}
t= \frac{34}{4} or  \frac{17}{2}
t=- \frac{17}{4}+ \frac{17}{4}
t=0
 \left \{ {{t= \frac{17}{2} } \atop {x=0}} \right.

3(x+2)^2=2x^2+3x-8
x^2+4x+4+3=2x^2+3x-8
 x^{2} -2 x^{2} +4x-3x+7+8=0
- x^{2} -x+15=0
 \frac{- x^{2} -x}{-1} = \frac{-15}{-1}
 x^{2} +x+( \frac{1}{2})^2 =15+( \frac{1}{2})^2
 \sqrt{(x+ \frac{1}{2})^2 } =+ or -  \sqrt{ \frac{61}{4} }
x+ \frac{1}{2} = +or- \sqrt{ \frac{61}{2}  } (When you write it on your paper don't include 2 in the square root sign)
x= \sqrt{ \frac{61-1}{2} } (Likewise here, don't include -1/2 in the square root sign)
x=- \sqrt{ \frac{61-1}{2} } (Here too)

5.Yes,
x^2+5x-14=0
(x+7)(x-2)=0
x+7=0
x-2=0
x=-7
x=2

14-5x-x^2=0
-1[14-5x-x^2=0]
Use distributive property then it will be equal to x²+5x-14=0.

(x-4)^2=9
 \sqrt{(x-4)^2} = \sqrt{9}
x-4=+or-3
x=3+4
x=7
x=-3+4
x=1

(x+4)^2=9
 x^{2} -8x+16-9=0
 x^{2} -8x+7=0
(x-7)(x-1)=0
x-7=0
x=7
x-1=0
x=1

P.S. Done at last... Sorry for the late answers.... Solving it was time consuming... Sorry also because I can't quite get number 7.... I hope this helps you though... :(

2 5 2
Armina arigatōgozaimashita :)
Doishimashite ^_^