What are the solutions to the equation 7a+2=-2a^2 ?

The solutions to the equation 7a+2=-2a^2 are a=-(7+sqrt(33))/4 ,a=-(7-sqrt(33))/4

Find the zeros of 7a+2=-2a^2

The zeros of 7a+2=-2a^2 are a=-(7+sqrt(33))/4 ,a=-(7-sqrt(33))/4

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7 a + 2 = - 2 a^{2}

a = - \frac{7 + 33}{4}, a = - \frac{7 - 33}{4}

Decimal Notation

a = - 3.18614 \dots, a = - 0.31385 \dots

Solution steps

7 a + 2 = - 2 a^{2}

Switch sides

- 2 a^{2} = 7 a + 2

Move

2

to the left side

- 2 a^{2} - 2 = 7 a

Move

7 a

to the left side

- 2 a^{2} - 2 - 7 a = 0

Write in the standard form

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

- 2 a^{2} - 7 a - 2 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 ( - 2 ) ( - 2 )}{2 ( - 2 )}

(- 7)^{2} - 4 (- 2) (- 2) = 33

a_{1, 2} = \frac{- ( - 7 ) \pm 33}{2 ( - 2 )}

Separate the solutions

a_{1} = \frac{- ( - 7 ) + 33}{2 ( - 2 )}, a_{2} = \frac{- ( - 7 ) - 33}{2 ( - 2 )}

a = \frac{- ( - 7 ) + 33}{2 ( - 2 )} : - \frac{7 + 33}{4}

a = \frac{- ( - 7 ) - 33}{2 ( - 2 )} : - \frac{7 - 33}{4}

The solutions to the quadratic equation are:

a = - \frac{7 + 33}{4}, a = - \frac{7 - 33}{4}

x^{2} + 7 x + \frac{33}{4} = 0

d^{2} - 6 d + 2 = 0

(m - 5) (m - 4) = - 9 m

9 n^{2} - 7 n - 4 = 0

25 m^{2} + 36 m + 9 = 6 m

What are the solutions to the equation 7a+2=-2a^2 ?
The solutions to the equation 7a+2=-2a^2 are a=-(7+sqrt(33))/4 ,a=-(7-sqrt(33))/4
Find the zeros of 7a+2=-2a^2
The zeros of 7a+2=-2a^2 are a=-(7+sqrt(33))/4 ,a=-(7-sqrt(33))/4