Solve 10x^(2)-20x-84=-4

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 2, x_{2} = 4

Evaluate

10 x^{2} - 20 x - 84 = - 4

Move the expression to the left side

10 x^{2} - 20 x - 80 = 0

Factor the expression

More Steps

Evaluate

10 x^{2} - 20 x - 80

Rewrite the expression

10 x^{2} - 10 \times 2 x - 10 \times 8

Factor out 10 from the expression

10 (x^{2} - 2 x - 8)

Factor the expression

More Steps

Evaluate

x^{2} - 2 x - 8

Rewrite the expression

x^{2} + (2 - 4) x - 8

Calculate

x^{2} + 2 x - 4 x - 8

Rewrite the expression

x \times x + x \times 2 - 4 x - 4 \times 2

Factor out x from the expression

x (x + 2) - 4 x - 4 \times 2

Factor out - 4 from the expression

x (x + 2) - 4 (x + 2)

Factor out x + 2 from the expression

(x - 4) (x + 2)

10 (x - 4) (x + 2)

10 (x - 4) (x + 2) = 0

Divide the terms

(x - 4) (x + 2) = 0

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

x - 4 = 0 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 4 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = 4 x = - 2

Solution

x_{1} = - 2, x_{2} = 4

Show Solution