What are the solutions to the equation ((x+2)^2)/(12)-((x+5)^2)/(30)=1 ?

The solutions to the equation ((x+2)^2)/(12)-((x+5)^2)/(30)=1 are x=sqrt(30),x=-sqrt(30)

Find the zeros of ((x+2)^2)/(12)-((x+5)^2)/(30)=1

The zeros of ((x+2)^2)/(12)-((x+5)^2)/(30)=1 are x=sqrt(30),x=-sqrt(30)

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\frac{( x + 2 ) ^{2}}{12} - \frac{( x + 5 ) ^{2}}{30} = 1

x = 30, x = - 30

Decimal Notation

x = 5.47722 \dots, x = - 5.47722 \dots

Solution steps

\frac{( x + 2 ) ^{2}}{12} - \frac{( x + 5 ) ^{2}}{30} = 1

Find Least Common Multiplier of

12, 30 : 60

Multiply by LCM=

60

\frac{( x + 2 ) ^{2}}{12} \cdot 60 - \frac{( x + 5 ) ^{2}}{30} \cdot 60 = 1 \cdot 60

Simplify

5 (x + 2)^{2} - 2 (x + 5)^{2} = 60

Expand

5 (x + 2)^{2} - 2 (x + 5)^{2} : 3 x^{2} - 30

3 x^{2} - 30 = 60

Move

60

to the left side

3 x^{2} - 90 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 \cdot 3 ( - 90 )}{2 \cdot 3}

0^{2} - 4 \cdot 3 (- 90) = 630

x_{1, 2} = \frac{- 0 \pm 6 30}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 0 + 6 30}{2 \cdot 3}, x_{2} = \frac{- 0 - 6 30}{2 \cdot 3}

x = \frac{- 0 + 6 30}{2 \cdot 3} : 30

x = \frac{- 0 - 6 30}{2 \cdot 3} : - 30

The solutions to the quadratic equation are:

x = 30, x = - 30

3 x^{2} + x + 9 = 0

(x + 4)^{2} = 100

s^{2} + 10 s + 34 = 0

- 4 x^{2} - 4 x + 1 = 0

6 x^{2} - 8 x = 1

What are the solutions to the equation ((x+2)^2)/(12)-((x+5)^2)/(30)=1 ?
The solutions to the equation ((x+2)^2)/(12)-((x+5)^2)/(30)=1 are x=sqrt(30),x=-sqrt(30)
Find the zeros of ((x+2)^2)/(12)-((x+5)^2)/(30)=1
The zeros of ((x+2)^2)/(12)-((x+5)^2)/(30)=1 are x=sqrt(30),x=-sqrt(30)