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

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 1, x_{2} = 3

Evaluate

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

Expand the expression

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Evaluate

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

Expand the expression

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Evaluate

(x + 1)^{2}

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

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

Calculate

x^{2} + 2 x + 1

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

Add the terms

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Evaluate

x^{2} + x^{2}

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

(1 + 1) x^{2}

Add the numbers

2 x^{2}

2 x^{2} + 2 x + 1

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

Expand the expression

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Evaluate

(x + 2)^{2}

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

x^{2} + 2 x \times 2 + 2^{2}

Calculate

x^{2} + 4 x + 4

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

Move the expression to the left side

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

Factor the expression

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Evaluate

x^{2} - 2 x - 3

Rewrite the expression

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

Calculate

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

Rewrite the expression

x \times x + x - 3 x - 3

Factor out x from the expression

x (x + 1) - 3 x - 3

Factor out - 3 from the expression

x (x + 1) - 3 (x + 1)

Factor out x + 1 from the expression

(x - 3) (x + 1)

(x - 3) (x + 1) = 0

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

x - 3 = 0 x + 1 = 0

Solve the equation for x

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Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 x + 1 = 0

Solve the equation for x

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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 = 3 x = - 1

Solution

x_{1} = - 1, x_{2} = 3

Show Solution