Solve 7x^2 - 9x - 10 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{5}{7}, x_{2} = 2

Alternative Form

x_{1} = - 0. \dot{7} 1428 \dot{5}, x_{2} = 2

Evaluate

7 x^{2} - 9 x - 10 = 0

Factor the expression

More Steps

Evaluate

7 x^{2} - 9 x - 10

Rewrite the expression

7 x^{2} + (5 - 14) x - 10

Calculate

7 x^{2} + 5 x - 14 x - 10

Rewrite the expression

x \times 7 x + x \times 5 - 2 \times 7 x - 2 \times 5

Factor out x from the expression

x (7 x + 5) - 2 \times 7 x - 2 \times 5

Factor out - 2 from the expression

x (7 x + 5) - 2 (7 x + 5)

Factor out 7 x + 5 from the expression

(x - 2) (7 x + 5)

(x - 2) (7 x + 5) = 0

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

x - 2 = 0 7 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 7 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

7 x + 5 = 0

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

7 x = 0 - 5

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

7 x = - 5

Divide both sides

\frac{7 x}{7} = \frac{- 5}{7}

Divide the numbers

x = \frac{- 5}{7}

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

x = - \frac{5}{7}

x = 2 x = - \frac{5}{7}

Solution

x_{1} = - \frac{5}{7}, x_{2} = 2

Alternative Form

x_{1} = - 0. \dot{7} 1428 \dot{5}, x_{2} = 2

Show Solution