What are the solutions to the equation 27d^4=18d^2 ?

The solutions to the equation 27d^4=18d^2 are d=0,d=-sqrt(2/3),d=sqrt(2/3)

Find the zeros of 27d^4=18d^2

The zeros of 27d^4=18d^2 are d=0,d=-sqrt(2/3),d=sqrt(2/3)

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27 d^{4} = 18 d^{2}

d = 0, d = - \frac{2}{3}, d = \frac{2}{3}

Decimal Notation

d = 0, d = - 0.81649 \dots, d = 0.81649 \dots

Solution steps

27 d^{4} = 18 d^{2}

Move

18 d^{2}

to the left side

27 d^{4} - 18 d^{2} = 0

Factor

27 d^{4} - 18 d^{2} : 9 d^{2} (3 d + 2) (3 d - 2)

9 d^{2} (3 d + 2) (3 d - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

d = 0 or 3 d + 2 = 0 or 3 d - 2 = 0

Solve

3 d + 2 = 0 : d = - \frac{2}{3}

Solve

3 d - 2 = 0 : d = \frac{2}{3}

The solutions are

d = 0, d = - \frac{2}{3}, d = \frac{2}{3}

x^{3} + 4 x^{2} - 6 = 0

3 x^{4} - 7 x^{2} - 6 = 0

4 x^{2} 8 x - 7 = 0

3 x^{3} + 12 x = 5 x^{2} + 20

b^{4} = 16.6

What are the solutions to the equation 27d^4=18d^2 ?
The solutions to the equation 27d^4=18d^2 are d=0,d=-sqrt(2/3),d=sqrt(2/3)
Find the zeros of 27d^4=18d^2
The zeros of 27d^4=18d^2 are d=0,d=-sqrt(2/3),d=sqrt(2/3)