Solve 4x^2-3x-18=x^2

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 2, x_{2} = 3

Evaluate

4 x^{2} - 3 x - 18 = x^{2}

Move the expression to the left side

3 x^{2} - 3 x - 18 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 3 x - 18

Rewrite the expression

3 x^{2} - 3 x - 3 \times 6

Factor out 3 from the expression

3 (x^{2} - x - 6)

Factor the expression

More Steps

Evaluate

x^{2} - x - 6

Rewrite the expression

x^{2} + (2 - 3) x - 6

Calculate

x^{2} + 2 x - 3 x - 6

Rewrite the expression

x \times x + x \times 2 - 3 x - 3 \times 2

Factor out x from the expression

x (x + 2) - 3 x - 3 \times 2

Factor out - 3 from the expression

x (x + 2) - 3 (x + 2)

Factor out x + 2 from the expression

(x - 3) (x + 2)

3 (x - 3) (x + 2)

3 (x - 3) (x + 2) = 0

Divide the terms

(x - 3) (x + 2) = 0

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

x - 3 = 0 x + 2 = 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 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 = 3 x = - 2

Solution

x_{1} = - 2, x_{2} = 3

Show Solution