Solve 3x^2 -19x -1400 =0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{56}{3}, x_{2} = 25

Alternative Form

x_{1} = - 18. \dot{6}, x_{2} = 25

Evaluate

3 x^{2} - 19 x - 1400 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 19 x - 1400

Rewrite the expression

3 x^{2} + (56 - 75) x - 1400

Calculate

3 x^{2} + 56 x - 75 x - 1400

Rewrite the expression

x \times 3 x + x \times 56 - 25 \times 3 x - 25 \times 56

Factor out x from the expression

x (3 x + 56) - 25 \times 3 x - 25 \times 56

Factor out - 25 from the expression

x (3 x + 56) - 25 (3 x + 56)

Factor out 3 x + 56 from the expression

(x - 25) (3 x + 56)

(x - 25) (3 x + 56) = 0

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

x - 25 = 0 3 x + 56 = 0

Solve the equation for x

More Steps

Evaluate

x - 25 = 0

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

x = 0 + 25

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

x = 25

x = 25 3 x + 56 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 56 = 0

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

3 x = 0 - 56

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

3 x = - 56

Divide both sides

\frac{3 x}{3} = \frac{- 56}{3}

Divide the numbers

x = \frac{- 56}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{56}{3}

x = 25 x = - \frac{56}{3}

Solution

x_{1} = - \frac{56}{3}, x_{2} = 25

Alternative Form

x_{1} = - 18. \dot{6}, x_{2} = 25

Show Solution