Solve (x-5)^2 4=16

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 3, x_{2} = 7

Evaluate

(x - 5)^{2} \times 4 = 16

Use the commutative property to reorder the terms

4 (x - 5)^{2} = 16

Expand the expression

More Steps

Evaluate

4 (x - 5)^{2}

Expand the expression

More Steps

Evaluate

(x - 5)^{2}

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

x^{2} - 2 x \times 5 + 5^{2}

Calculate

x^{2} - 10 x + 25

4 (x^{2} - 10 x + 25)

Apply the distributive property

4 x^{2} - 4 \times 10 x + 4 \times 25

Multiply the numbers

4 x^{2} - 40 x + 4 \times 25

Multiply the numbers

4 x^{2} - 40 x + 100

4 x^{2} - 40 x + 100 = 16

Move the expression to the left side

4 x^{2} - 40 x + 84 = 0

Factor the expression

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Evaluate

4 x^{2} - 40 x + 84

Rewrite the expression

4 x^{2} - 4 \times 10 x + 4 \times 21

Factor out 4 from the expression

4 (x^{2} - 10 x + 21)

Factor the expression

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Evaluate

x^{2} - 10 x + 21

Rewrite the expression

x^{2} + (- 3 - 7) x + 21

Calculate

x^{2} - 3 x - 7 x + 21

Rewrite the expression

x \times x - x \times 3 - 7 x + 7 \times 3

Factor out x from the expression

x (x - 3) - 7 x + 7 \times 3

Factor out - 7 from the expression

x (x - 3) - 7 (x - 3)

Factor out x - 3 from the expression

(x - 7) (x - 3)

4 (x - 7) (x - 3)

4 (x - 7) (x - 3) = 0

Divide the terms

(x - 7) (x - 3) = 0

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

x - 7 = 0 x - 3 = 0

Solve the equation for x

More Steps

Evaluate

x - 7 = 0

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

x = 0 + 7

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

x = 7

x = 7 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 = 7 x = 3

Solution

x_{1} = 3, x_{2} = 7

Show Solution