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Popular >

41/144 x^2+1= 60/7 x-444/7

Solution

\frac{41}{144} x^{2} + 1 = \frac{60}{7} x - \frac{444}{7}

Solution

x = \frac{12 ( 360 + 163 )}{287}, x = \frac{12 ( 360 - 163 )}{287}

+1

Decimal Notation

x = 15.58608 \dots, x = 14.51844 \dots

Solution steps

\frac{41}{144} x^{2} + 1 = \frac{60}{7} x - \frac{444}{7}

Find Least Common Multiplier of

144, 7 : 1008

Multiply by LCM=

1008

\frac{41}{144} x^{2} \cdot 1008 + 1 \cdot 1008 = \frac{60}{7} x \cdot 1008 - \frac{444}{7} \cdot 1008

Simplify

287 x^{2} + 1008 = 8640 x - 63936

Move

63936

to the left side

287 x^{2} + 64944 = 8640 x

Move

8640 x

to the left side

287 x^{2} + 64944 - 8640 x = 0

Write in the standard form

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

287 x^{2} - 8640 x + 64944 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8640 ) \pm ( - 8640 ) ^{2} - 4 \cdot 287 \cdot 64944}{2 \cdot 287}

(- 8640)^{2} - 4 \cdot 287 \cdot 64944 = 24163

x_{1, 2} = \frac{- ( - 8640 ) \pm 24 163}{2 \cdot 287}

Separate the solutions

x_{1} = \frac{- ( - 8640 ) + 24 163}{2 \cdot 287}, x_{2} = \frac{- ( - 8640 ) - 24 163}{2 \cdot 287}

x = \frac{- ( - 8640 ) + 24 163}{2 \cdot 287} : \frac{12 ( 360 + 163 )}{287}

x = \frac{- ( - 8640 ) - 24 163}{2 \cdot 287} : \frac{12 ( 360 - 163 )}{287}

The solutions to the quadratic equation are:

x = \frac{12 ( 360 + 163 )}{287}, x = \frac{12 ( 360 - 163 )}{287}

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