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

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Evaluate

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

Expand the expression

More Steps

Evaluate

(2 x + 1)^{2}

Use (a + b)^{2} = a^{2} + 2 ab + b^{2} to expand the expression

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

Calculate

4 x^{2} + 4 x + 1

4 x^{2} + 4 x + 1 = (x - 1)^{2}

Expand the expression

More Steps

Use the the distributive property to expand the expression

x \times x + x (- 1) - x - (- 1)

Multiply the terms

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

Multiplying or dividing an odd number of negative terms equals a negative

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

When there is - in front of an expression in parentheses change the sign of each term of the expression and remove the parentheses

x^{2} - x - x + 1

Calculate

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Evaluate

- x - x

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

(- 1 - 1) x

Subtract the numbers

- 2 x

x^{2} - 2 x + 1

4 x^{2} + 4 x + 1 = x^{2} - 2 x + 1

Move the expression to the left side

3 x^{2} + 6 x = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 6 x

Rewrite the expression

3 x \times x + 3 x \times 2

Factor out 3 x from the expression

3 x (x + 2)

3 x (x + 2) = 0

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

3 x = 0 x + 2 = 0

Solve the equation for x

x = 0 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 = 0 x = - 2

Solution

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

Show Solution