Solve Using the Quadratic Formula 3x^2+5x=2

Problem

3 x squared plus 5 x equals 2

Solution

1. Rearrange the equation into standard form a x squared plus b x plus c equals 0 by subtracting 2 from both sides.

3 x squared plus 5 x minus 2 equals 0

2. Identify the coefficients a b and c for the quadratic formula.

a equals 3

b equals 5

c equals negative 2

3. Apply the quadratic formula x equals the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c and denominator 2 a by substituting the identified values.

x equals the fraction with numerator negative 5 plus or minus the square root of 5 squared minus 4 times 3 times negative 2 and denominator 2 times 3

4. Simplify the expression inside the square root (the discriminant).

x equals the fraction with numerator negative 5 plus or minus the square root of 25 plus 24 and denominator 6

x equals the fraction with numerator negative 5 plus or minus the square root of 49 and denominator 6

5. Evaluate the square root and solve for both possible values of x

x equals the fraction with numerator negative 5 plus or minus 7 and denominator 6

6. Calculate the first solution using the plus sign.

x equals the fraction with numerator negative 5 plus 7 and denominator 6 equals two sixths equals one third

7. Calculate the second solution using the minus sign.

x equals the fraction with numerator negative 5 minus 7 and denominator 6 equals negative 12 over 6 equals negative 2

Final Answer

x equals one third comma negative 2

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