1/4 x+4=-9x^2+2

Solution

\frac{1}{4} x + 4 = - 9 x^{2} + 2

x = - \frac{1}{72} - i \frac{1151}{72}, x = - \frac{1}{72} + i \frac{1151}{72}

Solution steps

\frac{1}{4} x + 4 = - 9 x^{2} + 2

Multiply both sides by

4

x + 16 = - 36 x^{2} + 8

Switch sides

- 36 x^{2} + 8 = x + 16

Move

16

to the left side

- 36 x^{2} - 8 = x

Move

x

to the left side

- 36 x^{2} - 8 - x = 0

Write in the standard form

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

- 36 x^{2} - x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( - 36 ) ( - 8 )}{2 ( - 36 )}

Simplify

(- 1)^{2} - 4 (- 36) (- 8) : 1151 i

x_{1, 2} = \frac{- ( - 1 ) \pm 1151 i}{2 ( - 36 )}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 1151 i}{2 ( - 36 )}, x_{2} = \frac{- ( - 1 ) - 1151 i}{2 ( - 36 )}

x = \frac{- ( - 1 ) + 1151 i}{2 ( - 36 )} : - \frac{1}{72} - i \frac{1151}{72}

x = \frac{- ( - 1 ) - 1151 i}{2 ( - 36 )} : - \frac{1}{72} + i \frac{1151}{72}

The solutions to the quadratic equation are:

x = - \frac{1}{72} - i \frac{1151}{72}, x = - \frac{1}{72} + i \frac{1151}{72}

(x^{2} + 6 x)^{\frac{1}{4}} < 2

- 3 x + 7 = 28

36 - z^{2} y^{2}

2 < ∣ c - 4 ∣

7 \geq 12 - g