Question

(2х+1)в квадрате-2(х-3)=(х+5)(4х-3)

Answer 1

4x²+4x+1-2x+6=4x²-3x+20x-15

4x²+4x+1-2x+6-4x²+3x-20x+15=0

4x-2x+3x-20x+1+6+15=0

-15x=-22

x= 22/15= 1 7/15

Answer 2

Let's start by expanding the left-hand side of the equation using the binomial formula:

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(2x + 1)² - 2(x - 3) = (x + 5)(4x - 3)

Expanding the left-hand side:

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(2x + 1)² = (2x + 1) * (2x + 1) = 4x² + 4x + 1

Now we can rewrite the equation as:

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4x² + 4x + 1 - 2(x - 3) = (x + 5)(4x - 3)

Simplifying the expression on the left-hand side:

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4x² + 4x + 1 - 2x + 6 = 4x² + 17x + 12

Combining like terms on both sides:

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2x² - 13x - 5 = 0

Now we can use the quadratic formula to solve for x:

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x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 2, b = -13, and c = -5. Substituting these values into the formula:

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x = (-(-13) ± sqrt((-13)² - 4(2)(-5))) / 2(2)

Simplifying the expression under the square root:

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x = (13 ± sqrt(169 + 40)) / 4
x = (13 ± sqrt(209)) / 4

These are the two solutions to the equation. They can be further simplified by using approximations or exact values for the square root of 209.