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To solve the equation 5x^2 + 4x + 1 + 3(1 - 3x), you can follow these steps:
Step 1: Simplify the equation by applying the distributive property:
5x^2 + 4x + 1 + 3 - 9x
Step 2: Combine like terms:
5x^2 - 5x + 4
Now, we have a quadratic equation in the form of ax^2 + bx + c, where a = 5, b = -5, and c = 4.
To find the solutions, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
x = (-(-5) ± √((-5)^2 - 4(5)(4))) / (2(5))
x = (5 ± √(25 - 80)) / 10
x = (5 ± √(-55)) / 10
Since the discriminant (b^2 - 4ac) is negative in this case, we can conclude that the equation has no real solutions.