What are the solutions to the equation (x^2)/7-x/(14)= 1/16 ?

The solutions to the equation (x^2)/7-x/(14)= 1/16 are x=(1+2sqrt(2))/4 ,x=(1-2sqrt(2))/4

Find the zeros of (x^2)/7-x/(14)= 1/16

The zeros of (x^2)/7-x/(14)= 1/16 are x=(1+2sqrt(2))/4 ,x=(1-2sqrt(2))/4

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\frac{x ^{2}}{7} - \frac{x}{14} = \frac{1}{16}

x = \frac{1 + 2 2}{4}, x = \frac{1 - 2 2}{4}

Decimal Notation

x = 0.95710 \dots, x = - 0.45710 \dots

Solution steps

\frac{x ^{2}}{7} - \frac{x}{14} = \frac{1}{16}

Find Least Common Multiplier of

7, 14, 16 : 112

Multiply by LCM=

112

\frac{x ^{2}}{7} \cdot 112 - \frac{x}{14} \cdot 112 = \frac{1}{16} \cdot 112

Simplify

16 x^{2} - 8 x = 7

Move

7

to the left side

16 x^{2} - 8 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 16 ( - 7 )}{2 \cdot 16}

(- 8)^{2} - 4 \cdot 16 (- 7) = 162

x_{1, 2} = \frac{- ( - 8 ) \pm 16 2}{2 \cdot 16}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 16 2}{2 \cdot 16}, x_{2} = \frac{- ( - 8 ) - 16 2}{2 \cdot 16}

x = \frac{- ( - 8 ) + 16 2}{2 \cdot 16} : \frac{1 + 2 2}{4}

x = \frac{- ( - 8 ) - 16 2}{2 \cdot 16} : \frac{1 - 2 2}{4}

The solutions to the quadratic equation are:

x = \frac{1 + 2 2}{4}, x = \frac{1 - 2 2}{4}

- 9 x^{2} = 108

- 3 x^{2} = - 15 x

6 x^{2} - 8 = 142

c^{2} - 3 c - 10 = 0

x, 2 x^{2} + 2 y^{2} + 12 x - 8 y + 31 = 0

What are the solutions to the equation (x^2)/7-x/(14)= 1/16 ?
The solutions to the equation (x^2)/7-x/(14)= 1/16 are x=(1+2sqrt(2))/4 ,x=(1-2sqrt(2))/4
Find the zeros of (x^2)/7-x/(14)= 1/16
The zeros of (x^2)/7-x/(14)= 1/16 are x=(1+2sqrt(2))/4 ,x=(1-2sqrt(2))/4