Solve 7x^2-48x-7=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{7}, x_{2} = 7

Alternative Form

x_{1} = - 0. \dot{1} 4285 \dot{7}, x_{2} = 7

Evaluate

7 x^{2} - 48 x - 7 = 0

Factor the expression

More Steps

Evaluate

7 x^{2} - 48 x - 7

Rewrite the expression

7 x^{2} + (1 - 49) x - 7

Calculate

7 x^{2} + x - 49 x - 7

Rewrite the expression

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

Factor out x from the expression

x (7 x + 1) - 7 \times 7 x - 7

Factor out - 7 from the expression

x (7 x + 1) - 7 (7 x + 1)

Factor out 7 x + 1 from the expression

(x - 7) (7 x + 1)

(x - 7) (7 x + 1) = 0

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

x - 7 = 0 7 x + 1 = 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 7 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

7 x + 1 = 0

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

7 x = 0 - 1

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

7 x = - 1

Divide both sides

\frac{7 x}{7} = \frac{- 1}{7}

Divide the numbers

x = \frac{- 1}{7}

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

x = - \frac{1}{7}

x = 7 x = - \frac{1}{7}

Solution

x_{1} = - \frac{1}{7}, x_{2} = 7

Alternative Form

x_{1} = - 0. \dot{1} 4285 \dot{7}, x_{2} = 7

Show Solution