Solve (x-3)^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{1}{3}, x_{2} = \frac{3}{11}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0. \dot{2} \dot{7}

Evaluate

(x - 3)^{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 - 3)^{2} = 100 x^{2}

Expand the expression

More Steps

Evaluate

(x - 3)^{2}

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

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

Calculate

x^{2} - 6 x + 9

x^{2} - 6 x + 9 = 100 x^{2}

Move the expression to the left side

- 99 x^{2} - 6 x + 9 = 0

Factor the expression

More Steps

Evaluate

- 99 x^{2} - 6 x + 9

Rewrite the expression

- 3 \times 33 x^{2} - 3 \times 2 x + 3 \times 3

Factor out - 3 from the expression

- 3 (33 x^{2} + 2 x - 3)

Factor the expression

More Steps

Evaluate

33 x^{2} + 2 x - 3

Rewrite the expression

33 x^{2} + (- 9 + 11) x - 3

Calculate

33 x^{2} - 9 x + 11 x - 3

Rewrite the expression

3 x \times 11 x - 3 x \times 3 + 11 x - 3

Factor out 3 x from the expression

3 x (11 x - 3) + 11 x - 3

Factor out 11 x - 3 from the expression

(3 x + 1) (11 x - 3)

- 3 (3 x + 1) (11 x - 3)

- 3 (3 x + 1) (11 x - 3) = 0

Divide the terms

(3 x + 1) (11 x - 3) = 0

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

11 x - 3 = 0 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

11 x - 3 = 0

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

11 x = 0 + 3

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

11 x = 3

Divide both sides

\frac{11 x}{11} = \frac{3}{11}

Divide the numbers

x = \frac{3}{11}

x = \frac{3}{11} 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 1 = 0

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

3 x = 0 - 1

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

3 x = - 1

Divide both sides

\frac{3 x}{3} = \frac{- 1}{3}

Divide the numbers

x = \frac{- 1}{3}

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

x = - \frac{1}{3}

x = \frac{3}{11} x = - \frac{1}{3}

Solution

x_{1} = - \frac{1}{3}, x_{2} = \frac{3}{11}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0. \dot{2} \dot{7}

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