What are the solutions to the equation 13744/100 x^2+54977/100 x+122500=0 ?

The solutions to the equation 13744/100 x^2+54977/100 x+122500=0 are

Find the zeros of 13744/100 x^2+54977/100 x+122500=0

The zeros of 13744/100 x^2+54977/100 x+122500=0 are

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\frac{13744}{100} x^{2} + \frac{54977}{100} x + 122500 = 0

x = - \frac{54977}{27488} + i \frac{\frac{3062500}{859} - \frac{5497 7 ^{2}}{188897536}}{2}, x = - \frac{54977}{27488} - i \frac{\frac{3062500}{859} - \frac{5497 7 ^{2}}{188897536}}{2}

Solution steps

\frac{13744}{100} x^{2} + \frac{54977}{100} x + 122500 = 0

Multiply both sides by

100

13744 x^{2} + 54977 x + 12250000 = 0

Divide both sides by

13744

\frac{13744 x ^{2}}{13744} + \frac{54977 x}{13744} + \frac{12250000}{13744} = \frac{0}{13744}

Write in the standard form

a x^{2} + b x + c = 0

x^{2} + \frac{54977 x}{13744} + \frac{765625}{859} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- \frac{54977}{13744} \pm ( \frac{54977}{13744} ) ^{2} - 4 \cdot 1 \cdot \frac{765625}{859}}{2 \cdot 1}

Simplify

(\frac{54977}{13744})^{2} - 4 \cdot 1 \cdot \frac{765625}{859} : i - \frac{5497 7 ^{2}}{188897536} + \frac{3062500}{859}

x_{1, 2} = \frac{- \frac{54977}{13744} \pm i - \frac{5497 7 ^{2}}{188897536} + \frac{3062500}{859}}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- \frac{54977}{13744} + i - \frac{5497 7 ^{2}}{188897536} + \frac{3062500}{859}}{2 \cdot 1}, x_{2} = \frac{- \frac{54977}{13744} - i - \frac{5497 7 ^{2}}{188897536} + \frac{3062500}{859}}{2 \cdot 1}

x = \frac{- \frac{54977}{13744} + i - \frac{5497 7 ^{2}}{188897536} + \frac{3062500}{859}}{2 \cdot 1} : - \frac{54977}{27488} + i \frac{\frac{3062500}{859} - \frac{5497 7 ^{2}}{188897536}}{2}

x = \frac{- \frac{54977}{13744} - i - \frac{5497 7 ^{2}}{188897536} + \frac{3062500}{859}}{2 \cdot 1} : - \frac{54977}{27488} - i \frac{\frac{3062500}{859} - \frac{5497 7 ^{2}}{188897536}}{2}

The solutions to the quadratic equation are:

x = - \frac{54977}{27488} + i \frac{\frac{3062500}{859} - \frac{5497 7 ^{2}}{188897536}}{2}, x = - \frac{54977}{27488} - i \frac{\frac{3062500}{859} - \frac{5497 7 ^{2}}{188897536}}{2}

218

(x + 4) (x + 5) = 0

(- \frac{5}{4})^{2}

(- \frac{1}{2})^{- 4}

\frac{9}{15 a - 15}

What are the solutions to the equation 13744/100 x^2+54977/100 x+122500=0 ?
The solutions to the equation 13744/100 x^2+54977/100 x+122500=0 are
Find the zeros of 13744/100 x^2+54977/100 x+122500=0
The zeros of 13744/100 x^2+54977/100 x+122500=0 are