Solve 4x^6-64x^4-x^2 16

Question

Simplify the expression

4 x^{6} - 64 x^{4} - 16 x^{2}

Show Solution

4 x^{2} (x^{4} - 16 x^{2} - 4)

Show Solution

x_{1} = - 8 + 217, x_{2} = 0, x_{3} = 8 + 217

Alternative Form

x_{1} \approx - 4.030659, x_{2} = 0, x_{3} \approx 4.030659

Evaluate

4 x^{6} - 64 x^{4} - x^{2} \times 16

To find the roots of the expression,set the expression equal to 0

4 x^{6} - 64 x^{4} - x^{2} \times 16 = 0

Use the commutative property to reorder the terms

4 x^{6} - 64 x^{4} - 16 x^{2} = 0

Factor the expression

4 x^{2} (x^{4} - 16 x^{2} - 4) = 0

Divide both sides

x^{2} (x^{4} - 16 x^{2} - 4) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{4} - 16 x^{2} - 4 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x^{4} - 16 x^{2} - 4 = 0

Solve the equation

More Steps

Evaluate

x^{4} - 16 x^{2} - 4 = 0

Solve the equation using substitution t = x^{2}

t^{2} - 16 t - 4 = 0

Substitute a= 1,b= - 16 and c= - 4 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{16 \pm ( - 16 ) ^{2} - 4 ( - 4 )}{2}

Simplify the expression

More Steps

t = \frac{16 \pm 272}{2}

Simplify the radical expression

More Steps

t = \frac{16 \pm 4 17}{2}

Separate the equation into 2 possible cases

t = \frac{16 + 4 17}{2} t = \frac{16 - 4 17}{2}

Simplify the expression

t = 8 + 217 t = \frac{16 - 4 17}{2}

Simplify the expression

t = 8 + 217 t = 8 - 217

Substitute back

x^{2} = 8 + 217 x^{2} = 8 - 217

Solve the equation for x

More Steps

x = 8 + 217 x = - 8 + 217 x^{2} = 8 - 217

Solve the equation for x

More Steps

x = 8 + 217 x = - 8 + 217 x = - 8 + 217 \times i x = - - 8 + 217 \times i

x = 0 x = 8 + 217 x = - 8 + 217

Solution

x_{1} = - 8 + 217, x_{2} = 0, x_{3} = 8 + 217

Alternative Form

x_{1} \approx - 4.030659, x_{2} = 0, x_{3} \approx 4.030659

Show Solution