What are the solutions to the equation (4x^2+3x-10)^2=9x^4 ?

The solutions to the equation (4x^2+3x-10)^2=9x^4 are x=1,x=2,x=-10/7 ,x=-5

Find the zeros of (4x^2+3x-10)^2=9x^4

The zeros of (4x^2+3x-10)^2=9x^4 are x=1,x=2,x=-10/7 ,x=-5

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

x = 1, x = 2, x = - \frac{10}{7}, x = - 5

Decimal Notation

x = 1, x = 2, x = - 1.42857 \dots, x = - 5

Solution steps

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

Expand

(4 x^{2} + 3 x - 10)^{2} : 16 x^{4} + 24 x^{3} - 71 x^{2} - 60 x + 100

16 x^{4} + 24 x^{3} - 71 x^{2} - 60 x + 100 = 9 x^{4}

Move

9 x^{4}

to the left side

7 x^{4} + 24 x^{3} - 71 x^{2} - 60 x + 100 = 0

Factor

7 x^{4} + 24 x^{3} - 71 x^{2} - 60 x + 100 : (x - 1) (x - 2) (7 x + 10) (x + 5)

(x - 1) (x - 2) (7 x + 10) (x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x - 2 = 0 or 7 x + 10 = 0 or x + 5 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

Solve

7 x + 10 = 0 : x = - \frac{10}{7}

Solve

x + 5 = 0 : x = - 5

The solutions are

x = 1, x = 2, x = - \frac{10}{7}, x = - 5

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

x^{12} - 3 = 9

81 x^{3} - 192 = 0

x^{3} - 5 x^{2} + 2 x + 14 = x^{2} - 3 x + 2

- x^{3} + 2 x^{2} + 2 x + 1 = 0

What are the solutions to the equation (4x^2+3x-10)^2=9x^4 ?
The solutions to the equation (4x^2+3x-10)^2=9x^4 are x=1,x=2,x=-10/7 ,x=-5
Find the zeros of (4x^2+3x-10)^2=9x^4
The zeros of (4x^2+3x-10)^2=9x^4 are x=1,x=2,x=-10/7 ,x=-5