Question

(2x + 1)²- (3 - x²) = 0​

Answer 1

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Answer 2

To solve the equation (2x + 1)² - (3 - x²) = 0, you can follow these steps:

1. Expand the square terms: (2x + 1)² = (2x + 1)(2x + 1) = 4x² + 4x + 1

2. Expand the second term and distribute the negative sign: -(3 - x²) = -3 + x²

So the equation becomes:

4x² + 4x + 1 - (3 - x²) = 0

3. Now, combine like terms:

4x² + 4x + 1 - 3 + x² = 0

4. Combine the x² terms:

5x² + 4x - 2 = 0

5. Now, this is a quadratic equation. You can solve it using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 5, b = 4, and c = -2. Plug these values into the quadratic formula:

x = (-4 ± √(4² - 4 * 5 * (-2))) / (2 * 5)

x = (-4 ± √(16 + 40)) / 10

x = (-4 ± √56) / 10

x = (-4 ± 2√14) / 10

Now, you can simplify further by dividing both the numerator and the denominator by 2:

x = (-2 ± √14) / 5

So, the solutions to the equation (2x + 1)² - (3 - x²) = 0 are:

x = (-2 + √14) / 5 x = (-2 - √14) / 5