Question

(5x-7) (8x+1)=(8x+1)до квадрата

Answer 1

(5x-7)(8x+1)=(8x+1)²

40x²-56x+5x-7=64x²+16x+1

40x²-51x-7=64x²+16x+1

40x²-51x-7-64x²-16x-1=0

-24x²-67x-8=0

24x²+67x+8=0

24x²+64x+3x+8=0

8x(3x+8)+3x+8=0

(3x+8)(8x+1)=0

x1=-8/3, x2=-1/8

x1=-2 2/8, x2=-1/8

Answer 2

To solve the equation, we'll expand the expression on the left side and simplify:

(5x - 7)(8x + 1) = (8x + 1)^2

Expanding the left side: 40x^2 - 35x - 56x + 7 = (8x + 1)^2

Simplifying the left side: 40x^2 - 91x + 7 = (8x + 1)^2

Expanding the right side: 40x^2 - 91x + 7 = 64x^2 + 16x + 1

Now, let's rearrange the equation and bring all terms to one side:

40x^2 - 91x + 7 - 64x^2 - 16x - 1 = 0

Simplifying further: -24x^2 - 107x + 6 = 0

This is a quadratic equation in standard form. To solve it, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -24, b = -107, and c = 6. Plugging these values into the quadratic formula:

x = (-(-107) ± √((-107)^2 - 4(-24)(6))) / (2(-24))

Simplifying inside the square root: x = (107 ± √(11449 + 576)) / (-48) x = (107 ± √12025) / (-48) x = (107 ± 109.75) / (-48)

This gives us two possible solutions:

x = (107 + 109.75) / (-48) ≈ -4.458 x = (107 - 109.75) / (-48) ≈ 0.031

Therefore, the equation (5x - 7)(8x + 1) = (8x + 1)^2 has two solutions: approximately x = -4.458 and x = 0.031.