What is the answer to 10pi=5+pisqrt(100-x^2) ?

The answer to 10pi=5+pisqrt(100-x^2) is x=(sqrt(100pi-25))/pi ,x=-(sqrt(100pi-25))/pi

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10pi=5+pisqrt(100-x^2)

10 π = 5 + π 100 - x^{2}

x = \frac{100 π - 25}{π}, x = - \frac{100 π - 25}{π}

Decimal Notation

x = 5.41275 \dots, x = - 5.41275 \dots

Solution steps

10 π = 5 + π 100 - x^{2}

Switch sides

5 + π 100 - x^{2} = 10 π

Move

5

to the right side

π 100 - x^{2} = 10 π - 5

Divide both sides by

π

100 - x^{2} = \frac{10 π - 5}{π}

Square both sides:

100 - x^{2} = 100 - \frac{100}{π} + \frac{25}{π ^{2}}

100 - x^{2} = 100 - \frac{100}{π} + \frac{25}{π ^{2}}

Solve

100 - x^{2} = 100 - \frac{100}{π} + \frac{25}{π ^{2}} : x = \frac{100 π - 25}{π}, x = - \frac{100 π - 25}{π}

x = \frac{100 π - 25}{π}, x = - \frac{100 π - 25}{π}

Verify Solutions:

x = \frac{100 π - 25}{π}

True

, x = - \frac{100 π - 25}{π}

True

The solutions are

x = \frac{100 π - 25}{π}, x = - \frac{100 π - 25}{π}

x^{2} - x - 2 = 0

2 x = - 9 x + 27 - 3

x + 4 - 3 x = 3

x + 2 + x + 7 = 5

2 \frac{1}{4} = x^{\frac{1}{2}}

What is the answer to 10pi=5+pisqrt(100-x^2) ?
The answer to 10pi=5+pisqrt(100-x^2) is x=(sqrt(100pi-25))/pi ,x=-(sqrt(100pi-25))/pi