Solve (x-1)^2 + x(x-1) + x^2

Question

Simplify the expression

3 x^{2} - 3 x + 1

Evaluate

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

Expand the expression

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

Expand the expression

More Steps

Calculate

x (x - 1)

Apply the distributive property

x \times x - x \times 1

Multiply the terms

x^{2} - x \times 1

Any expression multiplied by 1 remains the same

x^{2} - x

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

Add the terms

More Steps

Evaluate

x^{2} + x^{2} + x^{2}

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

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

Add the numbers

3 x^{2}

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

Solution

More Steps

Evaluate

- 2 x - x

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

(- 2 - 1) x

Subtract the numbers

- 3 x

3 x^{2} - 3 x + 1

Show Solution

Find the roots

x_{1} = \frac{1}{2} - \frac{3}{6} i, x_{2} = \frac{1}{2} + \frac{3}{6} i

Alternative Form

x_{1} \approx 0.5 - 0.288675 i, x_{2} \approx 0.5 + 0.288675 i

Evaluate

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

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

(x - 1)^{2} + x (x - 1) + x^{2} = 0

Calculate

More Steps

Evaluate

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

Expand the expression

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

Expand the expression

More Steps

Calculate

x (x - 1)

Apply the distributive property

x \times x - x \times 1

Multiply the terms

x^{2} - x \times 1

Any expression multiplied by 1 remains the same

x^{2} - x

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

Add the terms

More Steps

Evaluate

x^{2} + x^{2} + x^{2}

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

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

Add the numbers

3 x^{2}

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

Subtract the terms

More Steps

Evaluate

- 2 x - x

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

(- 2 - 1) x

Subtract the numbers

- 3 x

3 x^{2} - 3 x + 1

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

Substitute a= 3,b= - 3 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 3}{2 \times 3}

Simplify the expression

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 3}{6}

Simplify the expression

More Steps

Evaluate

(- 3)^{2} - 4 \times 3

Multiply the numbers

(- 3)^{2} - 12

Rewrite the expression

3^{2} - 12

Evaluate the power

9 - 12

Subtract the numbers

- 3

x = \frac{3 \pm - 3}{6}

Simplify the radical expression

More Steps

Evaluate

- 3

Evaluate the power

3 \times - 1

Evaluate the power

3 \times i

x = \frac{3 \pm 3 \times i}{6}

Separate the equation into 2 possible cases

x = \frac{3 + 3 \times i}{6} x = \frac{3 - 3 \times i}{6}

Simplify the expression

x = \frac{1}{2} + \frac{3}{6} i x = \frac{3 - 3 \times i}{6}

Simplify the expression

x = \frac{1}{2} + \frac{3}{6} i x = \frac{1}{2} - \frac{3}{6} i

Solution

x_{1} = \frac{1}{2} - \frac{3}{6} i, x_{2} = \frac{1}{2} + \frac{3}{6} i

Alternative Form

x_{1} \approx 0.5 - 0.288675 i, x_{2} \approx 0.5 + 0.288675 i

Show Solution