Solve 7( (-1)/2 x-1) 4/5 x=-3x-1

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{13 + 449}{28}, x_{2} = \frac{- 13 + 449}{28}

Alternative Form

x_{1} \approx - 1.221058, x_{2} \approx 0.292486

Evaluate

7 (\frac{- 1}{2} x - 1) \times \frac{4}{5} x = - 3 x - 1

Simplify

More Steps

\frac{28}{5} x (- \frac{1}{2} x - 1) = - 3 x - 1

Expand the expression

More Steps

- \frac{14}{5} x^{2} - \frac{28}{5} x = - 3 x - 1

Move the expression to the left side

- \frac{14}{5} x^{2} - \frac{13}{5} x + 1 = 0

Multiply both sides

\frac{14}{5} x^{2} + \frac{13}{5} x - 1 = 0

Multiply both sides

5 (\frac{14}{5} x^{2} + \frac{13}{5} x - 1) = 5 \times 0

Calculate

14 x^{2} + 13 x - 5 = 0

Substitute a= 14,b= 13 and c= - 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 13 \pm 1 3 ^{2} - 4 \times 14 ( - 5 )}{2 \times 14}

Simplify the expression

x = \frac{- 13 \pm 1 3 ^{2} - 4 \times 14 ( - 5 )}{28}

Simplify the expression

More Steps

x = \frac{- 13 \pm 449}{28}

Separate the equation into 2 possible cases

x = \frac{- 13 + 449}{28} x = \frac{- 13 - 449}{28}

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

x = \frac{- 13 + 449}{28} x = - \frac{13 + 449}{28}

Solution

x_{1} = - \frac{13 + 449}{28}, x_{2} = \frac{- 13 + 449}{28}

Alternative Form

x_{1} \approx - 1.221058, x_{2} \approx 0.292486

Show Solution