Solve each equation using the Quadratic Formula.
3x^2+5x=2
2x^2+5x-2=0
x=(-5+-sqrt(25-24))/6
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To solve the equation 3x^2 + 5x = 2 using the quadratic formula, we need to follow these steps:
Step 1: Write down the equation in the standard quadratic form, "ax^2 + bx + c = 0."
In this case, the equation is already in standard form: 3x^2 + 5x - 2 = 0.
Step 2: Identify the values of a, b, and c from the quadratic equation.
From our equation, a = 3, b = 5, and c = -2.
Step 3: Substitute the values for a, b, and c into the quadratic formula.
The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get: x = ( -5 ± √(5^2 - 4*(3)*(-2))) / (2*3)
Step 4: Simplify and solve the quadratic formula.
x = ( -5 ± √(25 + 24)) / 6
x = ( -5 ± √49) / 6
x = ( -5 ± 7) / 6
This gives us two possible solutions:
x₁ = (-5 + 7) / 6 = 2/6 = 1/3
x₂ = (-5 - 7) / 6 = -12/6 = -2
Therefore, the solutions to the equation 3x^2 + 5x = 2 are x = 1/3 and x = -2.