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Popular Algebra >

2.93^2=19.82^2+(24x)^2+((10)/pi x)^2

Solution

2.9 3^{2} = 19.8 2^{2} + (24 x)^{2} + (\frac{10}{π} x)^{2}

Solution

x = i \frac{384.2475 π 100 + 576 π ^{2}}{100 + 576 π ^{2}}, x = - i \frac{384.2475 π 100 + 576 π ^{2}}{100 + 576 π ^{2}}

Solution steps

2.9 3^{2} = 19.8 2^{2} + (24 x)^{2} + (\frac{10}{π} x)^{2}

Expand

2.9 3^{2} : 8.5849

Expand

19.8 2^{2} + (24 x)^{2} + (\frac{10}{π} x)^{2} : 392.8324 + \frac{576 π ^{2} + 100}{π ^{2}} x^{2}

8.5849 = 392.8324 + \frac{576 π ^{2} + 100}{π ^{2}} x^{2}

Switch sides

392.8324 + \frac{576 π ^{2} + 100}{π ^{2}} x^{2} = 8.5849

Move

392.8324

to the right side

\frac{576 π ^{2} + 100}{π ^{2}} x^{2} = - 384.2475

Multiply both sides by

π^{2}

(576 π^{2} + 100) x^{2} = - 384.2475 π^{2}

Divide both sides by

576 π^{2} + 100

x^{2} = - \frac{384.2475 π ^{2}}{576 π ^{2} + 100}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = - \frac{384.2475 π ^{2}}{576 π ^{2} + 100}, x = - - \frac{384.2475 π ^{2}}{576 π ^{2} + 100}

Simplify

- \frac{384.2475 π ^{2}}{576 π ^{2} + 100} : i \frac{384.2475 π 100 + 576 π ^{2}}{100 + 576 π ^{2}}

Simplify

- - \frac{384.2475 π ^{2}}{576 π ^{2} + 100} : - i \frac{384.2475 π 100 + 576 π ^{2}}{100 + 576 π ^{2}}

x = i \frac{384.2475 π 100 + 576 π ^{2}}{100 + 576 π ^{2}}, x = - i \frac{384.2475 π 100 + 576 π ^{2}}{100 + 576 π ^{2}}

Graph

Popular Examples

4=x^1*4.55+x^2*3.72

4 = x^{1} \cdot 4.55 + x^{2} \cdot 3.72

- 2 - 5 c^{2} = - 92

c^{2} = - 10 c

x^{2} = 1 - 2 x

20 = \frac{n ( n - 3 )}{2}

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