Algebra • Step-by-Step

Solve 3x² + 10x + 3 = 0 with Steps

Step-by-step solution for 3x² + 10x + 3 = 0. Factors into (3x + 1)(x + 3) = 0 to yield roots x = -1/3 and x = -3.

Problem Statement

3x^2 + 10x + 3 = 0

Final Result

x_1 = -3, \quad x_2 = -\frac{1}{3}

Formula Required: Quadratic Formula with a = 3

√64 = 8. x = (-10 + 8)/6 = -2/6 = -1/3, and x = (-10 - 8)/6 = -3.

x = \frac{-10 \pm \sqrt{10^2 - 4(3)(3)}}{2(3)} = \frac{-10 \pm \sqrt{64}}{6}

5 Steps

Write the equation in standard quadratic form $ax^2 + bx + c = 0$.

3x^2 + 10x + 3 = 0

Apply the $ac$ factoring method: find two numbers that multiply to $ac = (3)(3) = 9$ and add up to $b = 10$.

(1) \times (9) = 9, \quad (1) + (9) = 10

Split the middle term $10x$ into $1x + (9)x$ and factor by grouping.

3x^2 + 1x + 9x + 3 = 0 \implies (3x + 1)(x + 3) = 0

Set each factor equal to zero and solve for $x$.

(3x + 1) = 0 \implies x_1 = -0.333333 \quad \text{or} \quad (x + 3) = 0 \implies x_2 = -3

Verify each root by substituting back into the original equation.

\text{Check } x = -0.333333: \; 3(-0.333333)^2 + 10(-0.333333) + 3 = 0.333333 - 3.333333 + 3 = 0 \;\checkmark \\[6pt] \text{Check } x = -3: \; 3(-3)^2 + 10(-3) + 3 = 27 - 30 + 3 = 0 \;\checkmark

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

x = -1/3 and x = -3.