Solve -3(-x^2)-x^4=-12

Question

Solve the equation

Solve for x

x_{1} = - \frac{6 + 2 57}{2}, x_{2} = \frac{6 + 2 57}{2}

Alternative Form

x_{1} \approx - 2.296719, x_{2} \approx 2.296719

Evaluate

- 3 (- x^{2}) - x^{4} = - 12

Multiply the numbers

3 x^{2} - x^{4} = - 12

Move the expression to the left side

3 x^{2} - x^{4} - (- 12) = 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^{4} + 12 = 0

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

3 t - t^{2} + 12 = 0

Rewrite in standard form

- t^{2} + 3 t + 12 = 0

Multiply both sides

t^{2} - 3 t - 12 = 0

Substitute a= 1,b= - 3 and c= - 12 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{3 \pm ( - 3 ) ^{2} - 4 ( - 12 )}{2}

Simplify the expression

More Steps

t = \frac{3 \pm 57}{2}

Separate the equation into 2 possible cases

t = \frac{3 + 57}{2} t = \frac{3 - 57}{2}

Substitute back

x^{2} = \frac{3 + 57}{2} x^{2} = \frac{3 - 57}{2}

Solve the equation for x

More Steps

x = \frac{6 + 2 57}{2} x = - \frac{6 + 2 57}{2} x^{2} = \frac{3 - 57}{2}

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 = \frac{6 + 2 57}{2} x = - \frac{6 + 2 57}{2} x \in / R

Find the union

x = \frac{6 + 2 57}{2} x = - \frac{6 + 2 57}{2}

Solution

x_{1} = - \frac{6 + 2 57}{2}, x_{2} = \frac{6 + 2 57}{2}

Alternative Form

x_{1} \approx - 2.296719, x_{2} \approx 2.296719

Show Solution

3( X^2) X^4= 12

Solve the equation

Graph