Solve 10x^2/256 - x - 9 = 0

Question

Solve the equation

x_{1} = \frac{64 - 8 154}{5}, x_{2} = \frac{64 + 8 154}{5}

Alternative Form

x_{1} \approx - 7.055478, x_{2} \approx 32.655478

Evaluate

(10 \times \frac{x ^{2}}{256}) - x - 9 = 0

Multiply the terms

More Steps

\frac{5 x ^{2}}{128} - x - 9 = 0

Multiply both sides of the equation by LCD

(\frac{5 x ^{2}}{128} - x - 9) \times 128 = 0 \times 128

Simplify the equation

More Steps

5 x^{2} - 128 x - 1152 = 0 \times 128

Any expression multiplied by 0 equals 0

5 x^{2} - 128 x - 1152 = 0

Substitute a= 5,b= - 128 and c= - 1152 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{128 \pm ( - 128 ) ^{2} - 4 \times 5 ( - 1152 )}{2 \times 5}

Simplify the expression

x = \frac{128 \pm ( - 128 ) ^{2} - 4 \times 5 ( - 1152 )}{10}

Simplify the expression

More Steps

x = \frac{128 \pm 39424}{10}

Simplify the radical expression

More Steps

x = \frac{128 \pm 16 154}{10}

Separate the equation into 2 possible cases

x = \frac{128 + 16 154}{10} x = \frac{128 - 16 154}{10}

Simplify the expression

More Steps

x = \frac{64 + 8 154}{5} x = \frac{128 - 16 154}{10}

Simplify the expression

More Steps

x = \frac{64 + 8 154}{5} x = \frac{64 - 8 154}{5}

Solution

x_{1} = \frac{64 - 8 154}{5}, x_{2} = \frac{64 + 8 154}{5}

Alternative Form

x_{1} \approx - 7.055478, x_{2} \approx 32.655478

Show Solution