Question

solve the following quadratic equation by factorisation method
x(2x+3) =35​

Answer 1

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x*(2*x-3)-(35)=0

Step 1:Factoring 2x^2-3x-35=0

Multiply the coefficient of the first term by the constant 2 • -35 = -70

Find two factors of -70 whose sum equals the coefficient of the middle term, which is -3 .

-70 + 1 = -69

-35 + 2 = -33

-14 + 5 = -9

-10 + 7 = -3 (this is it)

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 7

2x^2 - 10x + 7x - 35

Add up the first 2 terms, pulling out like factors :

2x • (x-5)

Add up the last 2 terms, pulling out common factors :

7 • (x-5)

Now,Add up the four terms

(2x+7) • (x-5)

Now equate one term to "0"

Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Now equate the other term to "0"

Solve : 2x+7 = 0

Subtract 7 from both sides of the equation :

2x = -7

Divide both sides of the equation by 2:

x = -7/2 = -3.500

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