Solve 2(x-1)^2-32=0

Question

2 (x - 1)^{2} - 32 = 0

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 3, x_{2} = 5

Evaluate

2 (x - 1)^{2} - 32 = 0

Expand the expression

More Steps

Evaluate

2 (x - 1)^{2} - 32

Expand the expression

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Evaluate

2 (x - 1)^{2}

Expand the expression

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

Apply the distributive property

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

Multiply the numbers

2 x^{2} - 4 x + 2 \times 1

Any expression multiplied by 1 remains the same

2 x^{2} - 4 x + 2

2 x^{2} - 4 x + 2 - 32

Subtract the numbers

2 x^{2} - 4 x - 30

2 x^{2} - 4 x - 30 = 0

Factor the expression

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Evaluate

2 x^{2} - 4 x - 30

Rewrite the expression

2 x^{2} - 2 \times 2 x - 2 \times 15

Factor out 2 from the expression

2 (x^{2} - 2 x - 15)

Factor the expression

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Evaluate

x^{2} - 2 x - 15

Rewrite the expression

x^{2} + (3 - 5) x - 15

Calculate

x^{2} + 3 x - 5 x - 15

Rewrite the expression

x \times x + x \times 3 - 5 x - 5 \times 3

Factor out x from the expression

x (x + 3) - 5 x - 5 \times 3

Factor out - 5 from the expression

x (x + 3) - 5 (x + 3)

Factor out x + 3 from the expression

(x - 5) (x + 3)

2 (x - 5) (x + 3)

2 (x - 5) (x + 3) = 0

Divide the terms

(x - 5) (x + 3) = 0

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

x - 5 = 0 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 x + 3 = 0

Solve the equation for x

More Steps

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 = 5 x = - 3

Solution

x_{1} = - 3, x_{2} = 5

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