Solve x ^ 4 - 13x ^ 2 + 36 = 0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x^{4}-13x^{2}+36=0$$

Solve for x

$x=-3$
$x=3$
$x=2$
$x=-2$

Steps Using the Quadratic Formula

Substitute $t$ for $x^{2}$.

$$t^{2}-13t+36=0$$

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 $a$, $-13$ for $b$, and $36$ for $c$ in the quadratic formula.

$$t=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 1\times 36}}{2}$$

Do the calculations.

$$t=\frac{13±5}{2}$$

Solve the equation $t=\frac{13±5}{2}$ when $±$ is plus and when $±$ is minus.

$$t=9$$ $$t=4$$

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

$$x=3$$ $$x=-3$$ $$x=2$$ $$x=-2$$