Solve 100x^2-100x-11=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{10}, x_{2} = \frac{11}{10}

Alternative Form

x_{1} = - 0.1, x_{2} = 1.1

Evaluate

100 x^{2} - 100 x - 11 = 0

Factor the expression

More Steps

Evaluate

100 x^{2} - 100 x - 11

Rewrite the expression

100 x^{2} + (10 - 110) x - 11

Calculate

100 x^{2} + 10 x - 110 x - 11

Rewrite the expression

10 x \times 10 x + 10 x - 11 \times 10 x - 11

Factor out 10 x from the expression

10 x (10 x + 1) - 11 \times 10 x - 11

Factor out - 11 from the expression

10 x (10 x + 1) - 11 (10 x + 1)

Factor out 10 x + 1 from the expression

(10 x - 11) (10 x + 1)

(10 x - 11) (10 x + 1) = 0

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

10 x - 11 = 0 10 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

10 x - 11 = 0

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

10 x = 0 + 11

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

10 x = 11

Divide both sides

\frac{10 x}{10} = \frac{11}{10}

Divide the numbers

x = \frac{11}{10}

x = \frac{11}{10} 10 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

10 x + 1 = 0

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

10 x = 0 - 1

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

10 x = - 1

Divide both sides

\frac{10 x}{10} = \frac{- 1}{10}

Divide the numbers

x = \frac{- 1}{10}

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

x = - \frac{1}{10}

x = \frac{11}{10} x = - \frac{1}{10}

Solution

x_{1} = - \frac{1}{10}, x_{2} = \frac{11}{10}

Alternative Form

x_{1} = - 0.1, x_{2} = 1.1

Show Solution