3x^2 +5x + 4 =0

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3x^2 +5x + 4 =0

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Identify coefficients: Identify the coefficients of the quadratic equation. The quadratic equation is in the form ax^2 + bx + c = 0. For the equation 3x^2 + 5x + 4 = 0, the coefficients are: a = 3, b = 5, and c = 4.Check factorability: Check if the quadratic equation can be factored easily. In this case, the equation 3x^2 + 5x + 4 does not factor easily into two binomials. Therefore, we will use the quadratic formula to find the solutions.Write quadratic formula: Write down the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). We will use this formula to find the values of x that satisfy the equation 3x^2 + 5x + 4 = 0.Substitute coefficients: Substitute the coefficients into the quadratic formula. Substitute a = 3, b = 5, and c = 4 into the quadratic formula to get x = (-(5) ± √((5)^2 - 4(3)(4))) / (2(3)).Simplify and calculate discriminant: Simplify under the square root and calculate the discriminant. Calculate the discriminant (b^2 - 4ac) = (5)^2 - 4(3)(4) = 25 - 48 = -23.Use complex numbers: Since the discriminant is negative, the solutions will be complex numbers. We can write the solutions as x = (-5 ± √(-23)) / 6. The square root of a negative number is an imaginary number, so we can express √(-23) as i√23, where i is the imaginary unit.Write final solutions: Write the final solutions. The solutions to the equation 3x^2 + 5x + 4 = 0 are x = (-5 + i√23) / 6 and x = (-5 - i√23) / 6.

$3x^2 +5x + 4 =0$

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3x2+5x+4=03x^2 +5x + 4 =03x2+5x+4=0

$3x^2 +5x + 4 =0$