Solve x^4+1/2x^2=17/8

$$\frac { x ^ { 4 } + 1 } { 2 x ^ { 2 } } = \frac { 17 } { 8 }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

$$x=\frac{1}{2}=0.5$$

$$x=2$$

$$x=-2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8x^{2}, the least common multiple of 2x^{2},8.

$$4\left(x^{4}+1\right)=17x^{2}$$

Use the distributive property to multiply 4 by x^{4}+1.

$$4x^{4}+4=17x^{2}$$

Subtract 17x^{2} from both sides.

$$4x^{4}+4-17x^{2}=0$$

Substitute t for x^{2}.

$$4t^{2}-17t+4=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 4 for a, -17 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 4\times 4}}{2\times 4}$$

Do the calculations.

$$t=\frac{17±15}{8}$$

Solve the equation t=\frac{17±15}{8} when ± is plus and when ± is minus.

$$t=4 t=\frac{1}{4}$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=2 x=-2 x=\frac{1}{2} x=-\frac{1}{2}$$