Solve 7(-x^2)-6x=5(-x-1)-3x

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} = 1

Alternative Form

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

Evaluate

7 (- x^{2}) - 6 x = 5 (- x - 1) - 3 x

Multiply the numbers

- 7 x^{2} - 6 x = 5 (- x - 1) - 3 x

Expand the expression

More Steps

Evaluate

5 (- x - 1) - 3 x

Multiply the terms

More Steps

Evaluate

5 (- x - 1)

Apply the distributive property

5 (- x) - 5 \times 1

Multiply the numbers

- 5 x - 5 \times 1

Any expression multiplied by 1 remains the same

- 5 x - 5

- 5 x - 5 - 3 x

Subtract the terms

More Steps

Evaluate

- 5 x - 3 x

Collect like terms by calculating the sum or difference of their coefficients

(- 5 - 3) x

Subtract the numbers

- 8 x

- 8 x - 5

- 7 x^{2} - 6 x = - 8 x - 5

Move the expression to the left side

- 7 x^{2} + 2 x + 5 = 0

Factor the expression

More Steps

Evaluate

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

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out - x from the expression

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

Factor out 7 x + 5 from the expression

(- x + 1) (7 x + 5)

(- x + 1) (7 x + 5) = 0

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

- x + 1 = 0 7 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

- x + 1 = 0

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

- x = 0 - 1

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

- x = - 1

Change the signs on both sides of the equation

x = 1

x = 1 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 = 1 x = - \frac{5}{7}

Solution

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

Alternative Form

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

Show Solution