Solve x^4-74x^2+1225=0

$${ x }^{ 4 } -74 { x }^{ 2 } +1225=0$$

Solve for x

$$x=-7$$

$$x=7$$

$$x=5$$

$$x=-5$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-74t+1225=0$$

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 1 for a, -74 for b, and 1225 for c in the quadratic formula.

$$t=\frac{-\left(-74\right)±\sqrt{\left(-74\right)^{2}-4\times 1\times 1225}}{2}$$

Do the calculations.

$$t=\frac{74±24}{2}$$

Solve the equation t=\frac{74±24}{2} when ± is plus and when ± is minus.

$$t=49 t=25$$

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

$$x=7 x=-7 x=5 x=-5$$