Solve the following equations for x :

1 > 8x² + 15 = 26x
2> x (2x + 5) = 25​

2 thoughts on “Solve the following equations for x :<br /><br />1 > 8x² + 15 = 26x<br />2> x (2x + 5) = 25​”

1. 1 > 8x² + 15 = 26x

   • (Writing as ax² + bx + c = 0)

   ➸ 8x² – 26x + 15 = 0

   ➸ 8x² – 20x – 6x + 15 = 0

   ➸ 4x (2x – 5) – 3(2x – 5) = 0

   ➸ (2x – 5) (4x – 3) = 0 (Factorising left side )

   ➸ 2x – 5 = 0 or 4x – 3 = 0 (Zero – product rule)

   ➸ x = 5/2 or x = 3/4

   ❖ Therefore,

   • Hence, the roots of the given equation are 5/2 , 3/4.

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   2 > x (2x + 5) = 25

   • (Writing as ax² + bx + c = 0)

   ➸ 2x² + 5x – 25 = 0

   ➸ 2x² + 10x – 5x – 25 = 0

   ➸ 2x (x + 5) – 5(x + 5) = 0

   ➸ (x + 5) (2x – 5) = 0 (Factorising left side )

   ➸ x + 5 = 0 or 2x – 5 = 0 (Zero – product rule)

   ➸ x = -5 or x = 5/2

   ❖ Therefore,

   • Hence, the roots of the given equation are –5 , 5/2.

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2. Step-by-step explanation:

   8x^2+26x+15=0

   {{15×15=120}}

   so…

   8x^2+(20+6)x+15=0

   8x^2+20x+6x+15=0

   4x(2x+5)+3(2x+5)=0

   (4x+3)(2x+5)

   x=-3/4,-5/2

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