Solve x^4/2-2100x^2-19800000=0

Question

Solve the equation

x_{1} = - 10 21 + 3489, x_{2} = 10 21 + 3489

Alternative Form

x_{1} \approx - 93.45589, x_{2} \approx 93.45589

Evaluate

\frac{x ^{4}}{2} - 2100 x^{2} - 19800000 = 0

Multiply both sides of the equation by LCD

(\frac{x ^{4}}{2} - 2100 x^{2} - 19800000) \times 2 = 0 \times 2

Simplify the equation

More Steps

x^{4} - 4200 x^{2} - 39600000 = 0 \times 2

Any expression multiplied by 0 equals 0

x^{4} - 4200 x^{2} - 39600000 = 0

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

t^{2} - 4200 t - 39600000 = 0

Substitute a= 1,b= - 4200 and c= - 39600000 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{4200 \pm ( - 4200 ) ^{2} - 4 ( - 39600000 )}{2}

Simplify the expression

More Steps

t = \frac{4200 \pm 420 0 ^{2} + 158400000}{2}

Simplify the radical expression

More Steps

t = \frac{4200 \pm 600 489}{2}

Separate the equation into 2 possible cases

t = \frac{4200 + 600 489}{2} t = \frac{4200 - 600 489}{2}

Simplify the expression

More Steps

t = 2100 + 300489 t = \frac{4200 - 600 489}{2}

Simplify the expression

More Steps

t = 2100 + 300489 t = 2100 - 300489

Substitute back

x^{2} = 2100 + 300489 x^{2} = 2100 - 300489

Solve the equation for x

More Steps

x = 10 21 + 3489 x = - 10 21 + 3489 x^{2} = 2100 - 300489

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x

x = 10 21 + 3489 x = - 10 21 + 3489 x \in / R

Find the union

x = 10 21 + 3489 x = - 10 21 + 3489

Solution

x_{1} = - 10 21 + 3489, x_{2} = 10 21 + 3489

Alternative Form

x_{1} \approx - 93.45589, x_{2} \approx 93.45589

Show Solution