Solve -2(5x-9) 2 = -187(-x^2)

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{10 + 4 427}{187}, x_{2} = \frac{- 10 + 4 427}{187}

Alternative Form

x_{1} \approx - 0.495486, x_{2} \approx 0.388534

Evaluate

- 2 (5 x - 9) \times 2 = - 187 (- x^{2})

Multiply the terms

- 4 (5 x - 9) = - 187 (- x^{2})

Multiply the numbers

- 4 (5 x - 9) = 187 x^{2}

Swap the sides

187 x^{2} = - 4 (5 x - 9)

Expand the expression

More Steps

187 x^{2} = - 20 x + 36

Move the expression to the left side

187 x^{2} + 20 x - 36 = 0

Substitute a= 187,b= 20 and c= - 36 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 20 \pm 2 0 ^{2} - 4 \times 187 ( - 36 )}{2 \times 187}

Simplify the expression

x = \frac{- 20 \pm 2 0 ^{2} - 4 \times 187 ( - 36 )}{374}

Simplify the expression

More Steps

x = \frac{- 20 \pm 27328}{374}

Simplify the radical expression

More Steps

x = \frac{- 20 \pm 8 427}{374}

Separate the equation into 2 possible cases

x = \frac{- 20 + 8 427}{374} x = \frac{- 20 - 8 427}{374}

Simplify the expression

More Steps

x = \frac{- 10 + 4 427}{187} x = \frac{- 20 - 8 427}{374}

Simplify the expression

More Steps

x = \frac{- 10 + 4 427}{187} x = - \frac{10 + 4 427}{187}

Solution

x_{1} = - \frac{10 + 4 427}{187}, x_{2} = \frac{- 10 + 4 427}{187}

Alternative Form

x_{1} \approx - 0.495486, x_{2} \approx 0.388534

Show Solution