Solve (x1-x1)^2 - x1(x1-1/2)

Question

Simplify the expression

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

Evaluate

(x \times 1 - x \times 1)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2})

Subtract the terms

0^{2} - x \times 1 \times (x \times 1 - \frac{1}{2})

Any expression multiplied by 1 remains the same

0^{2} - x \times 1 \times (x - \frac{1}{2})

Calculate

0 - x \times 1 \times (x - \frac{1}{2})

Multiply the terms

0 - x (x - \frac{1}{2})

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

- x (x - \frac{1}{2})

Apply the distributive property

- x \times x - (- x \times \frac{1}{2})

Multiply the terms

- x^{2} - (- x \times \frac{1}{2})

Use the commutative property to reorder the terms

- x^{2} - (- \frac{1}{2} x)

Solution

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

Show Solution

- \frac{1}{2} x (2 x - 1)

Evaluate

(x \times 1 - x \times 1)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2})

Any expression multiplied by 1 remains the same

(x - x \times 1)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2})

Any expression multiplied by 1 remains the same

(x - x)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2})

Subtract the terms

0^{2} - x \times 1 \times (x \times 1 - \frac{1}{2})

Any expression multiplied by 1 remains the same

0^{2} - x \times 1 \times (x - \frac{1}{2})

Calculate

0 - x \times 1 \times (x - \frac{1}{2})

Multiply the terms

0 - x (x - \frac{1}{2})

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

- x (x - \frac{1}{2})

Factor the expression

- x \times \frac{1}{2} (2 x - 1)

Solution

- \frac{1}{2} x (2 x - 1)

Show Solution

x_{1} = 0, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.5

Evaluate

(x \times 1 - x \times 1)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2})

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

(x \times 1 - x \times 1)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2}) = 0

Any expression multiplied by 1 remains the same

(x - x \times 1)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2}) = 0

Any expression multiplied by 1 remains the same

(x - x)^{2} - x \times 1 \times (x \times 1 - \frac{1}{2}) = 0

Subtract the terms

0^{2} - x \times 1 \times (x \times 1 - \frac{1}{2}) = 0

Any expression multiplied by 1 remains the same

0^{2} - x \times 1 \times (x - \frac{1}{2}) = 0

Calculate

0 - x \times 1 \times (x - \frac{1}{2}) = 0

Multiply the terms

0 - x (x - \frac{1}{2}) = 0

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

- x (x - \frac{1}{2}) = 0

Change the sign

x (x - \frac{1}{2}) = 0

Separate the equation into 2 possible cases

x = 0 x - \frac{1}{2} = 0

Solve the equation

More Steps

Evaluate

x - \frac{1}{2} = 0

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

x = 0 + \frac{1}{2}

Add the terms

x = \frac{1}{2}

x = 0 x = \frac{1}{2}

Solution

x_{1} = 0, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.5

Show Solution