Solve (x-5)^2=(x 10)^2

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{5}{9}, x_{2} = \frac{5}{11}

Alternative Form

x_{1} = - 0. \dot{5}, x_{2} = 0. \dot{4} \dot{5}

Evaluate

(x - 5)^{2} = (x \times 10)^{2}

Simplify

More Steps

Evaluate

(x \times 10)^{2}

Use the commutative property to reorder the terms

(10 x)^{2}

To raise a product to a power,raise each factor to that power

1 0^{2} x^{2}

Evaluate the power

100 x^{2}

(x - 5)^{2} = 100 x^{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

x^{2} - 10 x + 25 = 100 x^{2}

Move the expression to the left side

- 99 x^{2} - 10 x + 25 = 0

Factor the expression

More Steps

Evaluate

- 99 x^{2} - 10 x + 25

Rewrite the expression

- 99 x^{2} + (45 - 55) x + 25

Calculate

- 99 x^{2} + 45 x - 55 x + 25

Rewrite the expression

- 9 x \times 11 x + 9 x \times 5 - 5 \times 11 x + 5 \times 5

Factor out - 9 x from the expression

- 9 x (11 x - 5) - 5 \times 11 x + 5 \times 5

Factor out - 5 from the expression

- 9 x (11 x - 5) - 5 (11 x - 5)

Factor out 11 x - 5 from the expression

(- 9 x - 5) (11 x - 5)

(- 9 x - 5) (11 x - 5) = 0

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

11 x - 5 = 0 - 9 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

11 x - 5 = 0

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

11 x = 0 + 5

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

11 x = 5

Divide both sides

\frac{11 x}{11} = \frac{5}{11}

Divide the numbers

x = \frac{5}{11}

x = \frac{5}{11} - 9 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

- 9 x - 5 = 0

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

- 9 x = 0 + 5

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

- 9 x = 5

Change the signs on both sides of the equation

9 x = - 5

Divide both sides

\frac{9 x}{9} = \frac{- 5}{9}

Divide the numbers

x = \frac{- 5}{9}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{5}{9}

x = \frac{5}{11} x = - \frac{5}{9}

Solution

x_{1} = - \frac{5}{9}, x_{2} = \frac{5}{11}

Alternative Form

x_{1} = - 0. \dot{5}, x_{2} = 0. \dot{4} \dot{5}

Show Solution