What are the solutions to the equation 1/8 x^2+1/4 x=2 ?

The solutions to the equation 1/8 x^2+1/4 x=2 are x=-1+sqrt(17),x=-1-sqrt(17)

Find the zeros of 1/8 x^2+1/4 x=2

The zeros of 1/8 x^2+1/4 x=2 are x=-1+sqrt(17),x=-1-sqrt(17)

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\frac{1}{8} x^{2} + \frac{1}{4} x = 2

x = - 1 + 17, x = - 1 - 17

Decimal Notation

x = 3.12310 \dots, x = - 5.12310 \dots

Solution steps

\frac{1}{8} x^{2} + \frac{1}{4} x = 2

Find Least Common Multiplier of

8, 4 : 8

Multiply by LCM=

8

\frac{1}{8} x^{2} \cdot 8 + \frac{1}{4} x \cdot 8 = 2 \cdot 8

Simplify

x^{2} + 2 x = 16

Move

16

to the left side

x^{2} + 2 x - 16 = 0

Solve with the quadratic formula

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

2^{2} - 4 \cdot 1 \cdot (- 16) = 217

x_{1, 2} = \frac{- 2 \pm 2 17}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 2 + 2 17}{2 \cdot 1}, x_{2} = \frac{- 2 - 2 17}{2 \cdot 1}

x = \frac{- 2 + 2 17}{2 \cdot 1} : - 1 + 17

x = \frac{- 2 - 2 17}{2 \cdot 1} : - 1 - 17

The solutions to the quadratic equation are:

x = - 1 + 17, x = - 1 - 17

x^{2} - 17 x = - 10 x - 6

- 15 x^{2} = 0

(a x + 2) (b x + 7) = 15 x^{2} + c x + 14

x^{2} - (m + 1) x - 5 = 0

200 - x = 60 + 0.2 x^{2}

What are the solutions to the equation 1/8 x^2+1/4 x=2 ?
The solutions to the equation 1/8 x^2+1/4 x=2 are x=-1+sqrt(17),x=-1-sqrt(17)
Find the zeros of 1/8 x^2+1/4 x=2
The zeros of 1/8 x^2+1/4 x=2 are x=-1+sqrt(17),x=-1-sqrt(17)