ML Aggarwal Solutions Class 9 Mathematics Solutions for Quadratic Equations Exercise 7 in Chapter 7 - Quadratic Equations

Question 3 Quadratic Equations Exercise 7

\text { (i) } x(2 x+5)=25

(ii) (x + 3) (x – 3) = 40

\text { (i) } x(2 x+5)=25

Let us simplify the given equation,

\begin{aligned} &2 x^{2}+5 x-25=0\\ &\text { By factorizing, we get }\\ &2 x^{2}+10 x-5 x-25=0 \end{aligned}

2x(x + 5) – 5 (x + 5) = 0

(x + 5) (2x - 5) = 0

So,

(x + 5) = 0 or (2x - 5) = 0

x = -5 or 2x = 5

x = -5 or x = 5/2

∴ Value of x = -5, 5/2

(ii) (x + 3) (x – 3) = 40

Let us simplify the given equation,

\begin{aligned} &\begin{array}{l} x^{2}-3 x+3 x-9=40 \\ x^{2}-9-40=0 \\ x^{2}-49=0 \\ x^{2}=49 \\ x=\sqrt{49} \\ \quad=\pm 7 \end{array}\\ &\therefore \text { Value of } x=7,-7 \end{aligned}

Video transcript
"hello students welcome to lido learning india's best online classroom our question for today is we need to solve these two given equation and find the value of x the first equation says that x in the bracket x plus 2 oh sorry 2 x plus 5 bracket close is equals to 25 that is x 2x plus 5 is equals to 25 right if we solve this equation we'll get the value as 2x square plus 5x minus 25 is equals to zero okay factorizing this equation will get it as 10 and 5 that is 2x squared plus 10x minus 5x minus 25 is equal to zero let's take the common so 2x is the common and in the bracket we will left with x plus 5 again here minus 5 is the common and in the bracket we are left with x plus 5 which is equals to 0 so what we are left with we are left with 2x minus 5 and in the another bracket we have x plus 5 whole equals to 0. so if 2x minus 5 is equals to 0 value of x will be 5 upon 2 and if x plus 5 is equals to 0 then value of x is yes it is minus 5. let's solve the next question the next part of this question says that x plus 3 x minus 3 is equals to 40. let's solve this equation first so it will be x square minus 3x plus 3x minus 9 is equals to 40 yeah or we can write it as x square minus 49 is equals to zero we can write it as x minus seven [Music] or x plus seven now you will be thinking why i have written this so it is from the property a square minus b square is equals to a minus b multiplied by a plus b okay so and 49 is b where b is 7 right 7 square in place of 49 we can write 7 square so if if x minus 7 is equal to 0 the value of x will be 7 and if x plus 7 is equals to 0 value of seven will be minus seven value of x will be minus seven so here we have two values of x that is plus and minus seven thank you so much i hope that this has solved all your doubts for more such questions do subscribe leader learning"
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