Solve 3x^2 * (x^2 - 5) = 5 - x^2

Question

Solve the equation

x_{1} = - 5, x_{2} = 5

Alternative Form

x_{1} \approx - 2.236068, x_{2} \approx 2.236068

Evaluate

3 x^{2} (x^{2} - 5) = 5 - x^{2}

Move the expression to the left side

3 x^{2} (x^{2} - 5) - (5 - x^{2}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

3 x^{2} (x^{2} - 5) - 5 + x^{2} = 0

Calculate the sum or difference

More Steps

Evaluate

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

Expand the expression

More Steps

Calculate

3 x^{2} (x^{2} - 5)

Apply the distributive property

3 x^{2} \times x^{2} - 3 x^{2} \times 5

Multiply the terms

3 x^{4} - 3 x^{2} \times 5

Multiply the numbers

3 x^{4} - 15 x^{2}

3 x^{4} - 15 x^{2} - 5 + x^{2}

Add the terms

More Steps

Evaluate

- 15 x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 15 + 1) x^{2}

Add the numbers

- 14 x^{2}

3 x^{4} - 14 x^{2} - 5

3 x^{4} - 14 x^{2} - 5 = 0

Factor the expression

(x^{2} - 5) (3 x^{2} + 1) = 0

Separate the equation into 2 possible cases

x^{2} - 5 = 0 3 x^{2} + 1 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 5 = 0

Move the constant to the right-hand side and change its sign

x^{2} = 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

x^{2} = 5

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 5

Separate the equation into 2 possible cases

x = 5 x = - 5

x = 5 x = - 5 3 x^{2} + 1 = 0

Solve the equation

More Steps

Evaluate

3 x^{2} + 1 = 0

Move the constant to the right-hand side and change its sign

3 x^{2} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

3 x^{2} = - 1

Divide both sides

\frac{3 x ^{2}}{3} = \frac{- 1}{3}

Divide the numbers

x^{2} = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{2} = - \frac{1}{3}

Calculate

x \in / R

x = 5 x = - 5 x \in / R

Find the union

x = 5 x = - 5

Solution

x_{1} = - 5, x_{2} = 5

Alternative Form

x_{1} \approx - 2.236068, x_{2} \approx 2.236068

Show Solution

Solve the equation

Graph