Solve 2x^2-3x+1 - ScanMath

Question

Factor the expression

(x - 1) (2 x - 1)

Evaluate

2 x^{2} - 3 x + 1

Rewrite the expression

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

Calculate

2 x^{2} - x - 2 x + 1

Rewrite the expression

x \times 2 x - x - 2 x + 1

Factor out x from the expression

x (2 x - 1) - 2 x + 1

Factor out - 1 from the expression

x (2 x - 1) - (2 x - 1)

Solution

(x - 1) (2 x - 1)

Show Solution

x_{1} = \frac{1}{2}, x_{2} = 1

Alternative Form

x_{1} = 0.5, x_{2} = 1

Evaluate

2 x^{2} - 3 x + 1

To find the roots of the expression,set the expression equal to 0

2 x^{2} - 3 x + 1 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 3 x + 1

Rewrite the expression

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

Calculate

2 x^{2} - x - 2 x + 1

Rewrite the expression

x \times 2 x - x - 2 x + 1

Factor out x from the expression

x (2 x - 1) - 2 x + 1

Factor out - 1 from the expression

x (2 x - 1) - (2 x - 1)

Factor out 2 x - 1 from the expression

(x - 1) (2 x - 1)

(x - 1) (2 x - 1) = 0

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

x - 1 = 0 2 x - 1 = 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

x = 1 2 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 1 x = \frac{1}{2}

Solution

x_{1} = \frac{1}{2}, x_{2} = 1

Alternative Form

x_{1} = 0.5, x_{2} = 1

Show Solution