Solve x^2-(x-1)^2=xⅹ2-1

Evaluate

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

Multiply

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

Swap the sides

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

Expand the expression

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

Move the expression to the left side

2 x^{2} - 2 x = 0

Factor the expression

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2 x (x - 1) = 0

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

x - 1 = 0 2 x = 0

Solve the equation for x

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x = 1 2 x = 0

Solve the equation for x

x = 1 x = 0

Solution

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

Solve the quadratic equation