What are the solutions to the equation ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5 ?

The solutions to the equation ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5 are x=-3,x=-1

Find the zeros of ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5

The zeros of ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5 are x=-3,x=-1

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\frac{( x + 2 ) ^{2}}{5} - \frac{( x ^{2} - 9 )}{4} = \frac{( x + 3 ) ^{2}}{2} + \frac{1}{5}

x = - 3, x = - 1

Solution steps

\frac{( x + 2 ) ^{2}}{5} - \frac{( x ^{2} - 9 )}{4} = \frac{( x + 3 ) ^{2}}{2} + \frac{1}{5}

Find Least Common Multiplier of

5, 4, 2 : 20

Multiply by LCM=

20

\frac{( x + 2 ) ^{2}}{5} \cdot 20 - \frac{x ^{2} - 9}{4} \cdot 20 = \frac{( x + 3 ) ^{2}}{2} \cdot 20 + \frac{1}{5} \cdot 20

Simplify

4 (x + 2)^{2} - 5 (x^{2} - 9) = 10 (x + 3)^{2} + 4

Expand

4 (x + 2)^{2} - 5 (x^{2} - 9) : - x^{2} + 16 x + 61

Expand

10 (x + 3)^{2} + 4 : 10 x^{2} + 60 x + 94

- x^{2} + 16 x + 61 = 10 x^{2} + 60 x + 94

Move

94

to the left side

- x^{2} + 16 x - 33 = 10 x^{2} + 60 x

Move

60 x

to the left side

- x^{2} - 44 x - 33 = 10 x^{2}

Move

10 x^{2}

to the left side

- 11 x^{2} - 44 x - 33 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 44 ) \pm ( - 44 ) ^{2} - 4 ( - 11 ) ( - 33 )}{2 ( - 11 )}

(- 44)^{2} - 4 (- 11) (- 33) = 22

x_{1, 2} = \frac{- ( - 44 ) \pm 22}{2 ( - 11 )}

Separate the solutions

x_{1} = \frac{- ( - 44 ) + 22}{2 ( - 11 )}, x_{2} = \frac{- ( - 44 ) - 22}{2 ( - 11 )}

x = \frac{- ( - 44 ) + 22}{2 ( - 11 )} : - 3

x = \frac{- ( - 44 ) - 22}{2 ( - 11 )} : - 1

The solutions to the quadratic equation are:

x = - 3, x = - 1

x, 4 x^{2} - 6 x y - 4 y^{2} = 15

w^{2} + w - 2 = 0

x^{2} + x - 30 = 0

3 x^{2} - 60 = 3 x

3 x^{2} + 12 = 7 x + 32

What are the solutions to the equation ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5 ?
The solutions to the equation ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5 are x=-3,x=-1
Find the zeros of ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5
The zeros of ((x+2)^2)/5-((x^2-9))/4 =((x+3)^2)/2+1/5 are x=-3,x=-1