Question

Solve the following equations for x :

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

Answer 1

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

Answer 2

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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