Question

1)x+2²-(5x+1)²=02)5(2x+1)²+4x²=1​

Answer 1

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Answer 2

Let's solve each equation step by step:

1. x + 2² - (5x + 1)² = 0

First, let's simplify the equation:

x + 4 - (25x² + 10x + 1) = 0

Combine like terms:

-25x² + x - 7 = 0

Now, we have a quadratic equation. We can solve it by factoring or using the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the equation -25x² + x - 7 = 0, the coefficients are:

a = -25 b = 1 c = -7

Substituting the values into the quadratic formula:

x = (-1 ± √(1² - 4(-25)(-7))) / (2(-25))

Simplifying further:

x = (-1 ± √(1 - 700)) / (-50)

x = (-1 ± √(-699)) / (-50)

Since the discriminant is negative (-699), the equation does not have any real solutions. Therefore, there are no real values for x that satisfy the equation.

2. 5(2x + 1)² + 4x² = 1

Expand and simplify the equation:

20x² + 20x + 5 + 4x² = 1

Combine like terms:

24x² + 20x + 4 = 1

Subtract 1 from both sides:

24x² + 20x + 3 = 0

Now, we have another quadratic equation. We can solve it using factoring or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the equation 24x² + 20x + 3 = 0, the coefficients are:

a = 24 b = 20 c = 3

Substituting the values into the quadratic formula:

x = (-20 ± √(20² - 4(24)(3))) / (2(24))

Simplifying further:

x = (-20 ± √(400 - 288)) / 48

x = (-20 ± √112) / 48

x = (-20 ± √(16 * 7)) / 48

x = (-20 ± 4√7) / 48

Simplifying the expression:

x = (-5 ± √7) / 12

Therefore, the solutions to the equation 5(2x + 1)² + 4x² = 1 are:

x = (-5 + √7) / 12

x = (-5 - √7) / 12