Solve (x)^(2)=2sqrt(42)+13 | 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

$${ x }^{ 2 } =2 \sqrt{ 42 } +13$$

Solve for x (complex solution)

$x=-\left(\sqrt{6}+\sqrt{7}\right)\approx -5.095241054$
$x=\sqrt{6}+\sqrt{7}\approx 5.095241054$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

The equation is now solved.

$$x=\sqrt{6}+\sqrt{7}$$ $$x=-\left(\sqrt{6}+\sqrt{7}\right)$$

Steps Using the Quadratic Formula

Subtract $2\sqrt{42}$ from both sides.

$$x^{2}-2\sqrt{42}=13$$

Subtract $13$ from both sides.

$$x^{2}-2\sqrt{42}-13=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-2\sqrt{42}-13$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\sqrt{42}-13\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-2\sqrt{42}-13\right)}}{2}$$

Multiply $-4$ times $-2\sqrt{42}-13$.

$$x=\frac{0±\sqrt{8\sqrt{42}+52}}{2}$$

Take the square root of $8\sqrt{42}+52$.

$$x=\frac{0±\left(2\sqrt{6}+2\sqrt{7}\right)}{2}$$

Now solve the equation $x=\frac{0±\left(2\sqrt{6}+2\sqrt{7}\right)}{2}$ when $±$ is plus.

$$x=\sqrt{6}+\sqrt{7}$$

Now solve the equation $x=\frac{0±\left(2\sqrt{6}+2\sqrt{7}\right)}{2}$ when $±$ is minus.

$$x=-\sqrt{6}-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{6}+\sqrt{7}$$ $$x=-\sqrt{6}-\sqrt{7}$$

Solve for x

$x=\sqrt{6}+\sqrt{7}\approx 5.095241054$
$x=-\sqrt{6}-\sqrt{7}\approx -5.095241054$