solvefor x,r(x)^2=(0.998-0.954x)/(213879)

Solution

solve for

x, r (x)^{2} = \frac{0.998 - 0.954 x}{213879}

x = \frac{- 0.954 + 0.910116 + 853804.968 r}{427758 r}, x = \frac{- 0.954 - 0.910116 + 853804.968 r}{427758 r}; r \neq = 0

Solution steps

r x^{2} = \frac{0.998 - 0.954 x}{213879}

Multiply both sides by

213879

213879 x^{2} r = 0.998 - 0.954 x

Move

0.954 x

to the left side

213879 x^{2} r + 0.954 x = 0.998

Move

0.998

to the left side

213879 x^{2} r + 0.954 x - 0.998 = 0

Write in the standard form

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

213879 r x^{2} + 0.954 x - 0.998 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 0.954 \pm 0.95 4 ^{2} - 4 \cdot 213879 r ( - 0.998 )}{2 \cdot 213879 r}

Simplify

0.95 4^{2} - 4 \cdot 213879 r (- 0.998) : 0.910116 + 853804.968 r

x_{1, 2} = \frac{- 0.954 \pm 0.910116 + 853804.968 r}{2 \cdot 213879 r}; r \neq = 0

Separate the solutions

x_{1} = \frac{- 0.954 + 0.910116 + 853804.968 r}{2 \cdot 213879 r}, x_{2} = \frac{- 0.954 - 0.910116 + 853804.968 r}{2 \cdot 213879 r}

x = \frac{- 0.954 + 0.910116 + 853804.968 r}{2 \cdot 213879 r} : \frac{- 0.954 + 0.910116 + 853804.968 r}{427758 r}

x = \frac{- 0.954 - 0.910116 + 853804.968 r}{2 \cdot 213879 r} : \frac{- 0.954 - 0.910116 + 853804.968 r}{427758 r}

The solutions to the quadratic equation are:

x = \frac{- 0.954 + 0.910116 + 853804.968 r}{427758 r}, x = \frac{- 0.954 - 0.910116 + 853804.968 r}{427758 r}; r \neq = 0

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