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