What is the answer to 2x^2-3=sqrt((x+3)/2) ?

The answer to 2x^2-3=sqrt((x+3)/2) is x= 3/2 ,x=-(1+sqrt(21))/4

Solve for x: 2x^2-3=sqrt((x+3)/2)

The solution is x= 3/2 ,x=-(1+sqrt(21))/4

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2 x^{2} - 3 = \frac{x + 3}{2}

x = \frac{3}{2}, x = - \frac{1 + 21}{4}

Decimal Notation

x = 1.5, x = - 1.39564 \dots

Solution steps

2 x^{2} - 3 = \frac{x + 3}{2}

Square both sides:

4 x^{4} - 12 x^{2} + 9 = \frac{x + 3}{2}

4 x^{4} - 12 x^{2} + 9 = \frac{x + 3}{2}

Solve

4 x^{4} - 12 x^{2} + 9 = \frac{x + 3}{2} : x = - 1, x = \frac{3}{2}, x = \frac{- 1 + 21}{4}, x = - \frac{1 + 21}{4}

x = - 1, x = \frac{3}{2}, x = \frac{- 1 + 21}{4}, x = - \frac{1 + 21}{4}

Verify Solutions:

x = - 1

False

, x = \frac{3}{2}

True

, x = \frac{- 1 + 21}{4}

False

, x = - \frac{1 + 21}{4}

True

The solutions are

x = \frac{3}{2}, x = - \frac{1 + 21}{4}

- x + 1 = x - 1

3 y + 2 = y^{2} + 10 y + 7

7 x^{\frac{9}{4}} + 13 = 70543885

2 - x^{2} = x^{2}

What is the answer to 2x^2-3=sqrt((x+3)/2) ?
The answer to 2x^2-3=sqrt((x+3)/2) is x= 3/2 ,x=-(1+sqrt(21))/4
Solve for x: 2x^2-3=sqrt((x+3)/2)
The solution is x= 3/2 ,x=-(1+sqrt(21))/4