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

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Evaluate

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

Subtract the terms

More Steps

Evaluate

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

Collect like terms by calculating the sum or difference of their coefficients

(3 - 4) x^{2}

Subtract the numbers

- x^{2}

- x^{2} = 2 x - 3

Move the expression to the left side

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

Factor the expression

More Steps

Evaluate

- x^{2} - 2 x + 3

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out - x from the expression

- x (x + 3) + x + 3

Factor out x + 3 from the expression

(- x + 1) (x + 3)

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

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

- x + 1 = 0 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

- x + 1 = 0

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

- x = 0 - 1

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

- x = - 1

Change the signs on both sides of the equation

x = 1

x = 1 x + 3 = 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 = 1 x = - 3

Solution

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

Show Solution