Solve 3x^2-10x=-3

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{1}{3}, x_{2} = 3

Alternative Form

x_{1} = 0. \dot{3}, x_{2} = 3

Evaluate

3 x^{2} - 10 x = - 3

Move the expression to the left side

3 x^{2} - 10 x + 3 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 10 x + 3

Rewrite the expression

3 x^{2} + (- 1 - 9) x + 3

Calculate

3 x^{2} - x - 9 x + 3

Rewrite the expression

x \times 3 x - x - 3 \times 3 x + 3

Factor out x from the expression

x (3 x - 1) - 3 \times 3 x + 3

Factor out - 3 from the expression

x (3 x - 1) - 3 (3 x - 1)

Factor out 3 x - 1 from the expression

(x - 3) (3 x - 1)

(x - 3) (3 x - 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 3 = 0 3 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

x = 3

x = 3 3 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 1 = 0

Move the constant to the right-hand side and change its sign

3 x = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = 3 x = \frac{1}{3}

Solution

x_{1} = \frac{1}{3}, x_{2} = 3

Alternative Form

x_{1} = 0. \dot{3}, x_{2} = 3

Show Solution