Solve 10x-10x^(2)-9=0

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

Show Solution

Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

x_{1} = \frac{1}{2} - \frac{65}{10} i, x_{2} = \frac{1}{2} + \frac{65}{10} i

Alternative Form

x_{1} \approx 0.5 - 0.806226 i, x_{2} \approx 0.5 + 0.806226 i

Evaluate

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

Rewrite in standard form

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

Multiply both sides

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

Substitute a= 10,b= - 10 and c= 9 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 10 \times 9}{2 \times 10}

Simplify the expression

x = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 10 \times 9}{20}

Simplify the expression

More Steps

x = \frac{10 \pm - 260}{20}

Simplify the radical expression

More Steps

x = \frac{10 \pm 2 65 \times i}{20}

Separate the equation into 2 possible cases

x = \frac{10 + 2 65 \times i}{20} x = \frac{10 - 2 65 \times i}{20}

Simplify the expression

More Steps

x = \frac{1}{2} + \frac{65}{10} i x = \frac{10 - 2 65 \times i}{20}

Simplify the expression

More Steps

x = \frac{1}{2} + \frac{65}{10} i x = \frac{1}{2} - \frac{65}{10} i

Solution

x_{1} = \frac{1}{2} - \frac{65}{10} i, x_{2} = \frac{1}{2} + \frac{65}{10} i

Alternative Form

x_{1} \approx 0.5 - 0.806226 i, x_{2} \approx 0.5 + 0.806226 i

Show Solution