Solve 4x^2 - 300x + 1400 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 5, x_{2} = 70

Evaluate

4 x^{2} - 300 x + 1400 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 300 x + 1400

Rewrite the expression

4 x^{2} - 4 \times 75 x + 4 \times 350

Factor out 4 from the expression

4 (x^{2} - 75 x + 350)

Factor the expression

More Steps

Evaluate

x^{2} - 75 x + 350

Rewrite the expression

x^{2} + (- 5 - 70) x + 350

Calculate

x^{2} - 5 x - 70 x + 350

Rewrite the expression

x \times x - x \times 5 - 70 x + 70 \times 5

Factor out x from the expression

x (x - 5) - 70 x + 70 \times 5

Factor out - 70 from the expression

x (x - 5) - 70 (x - 5)

Factor out x - 5 from the expression

(x - 70) (x - 5)

4 (x - 70) (x - 5)

4 (x - 70) (x - 5) = 0

Divide the terms

(x - 70) (x - 5) = 0

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

x - 70 = 0 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 70 = 0

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

x = 0 + 70

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

x = 70

x = 70 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 70 x = 5

Solution

x_{1} = 5, x_{2} = 70

Show Solution