Solve (x)^(2)-3=2sqrt(2) | 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

$${ x }^{ 2 } -3=2 \sqrt{ 2 }$$

Solve for x (complex solution)

$x=-\left(\sqrt{2}+1\right)\approx -2.414213562$
$x=\sqrt{2}+1\approx 2.414213562$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $3$ to both sides.

$$x^{2}=2\sqrt{2}+3$$

The equation is now solved.

$$x=\sqrt{2}+1$$ $$x=-\left(\sqrt{2}+1\right)$$

Steps Using the Quadratic Formula

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

$$x^{2}-3-2\sqrt{2}=0$$

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

$$x^{2}-2\sqrt{2}-3=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-3-2\sqrt{2}$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\sqrt{2}-3\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-2\sqrt{2}-3\right)}}{2}$$

Multiply $-4$ times $-3-2\sqrt{2}$.

$$x=\frac{0±\sqrt{8\sqrt{2}+12}}{2}$$

Take the square root of $12+2^{\frac{7}{2}}$.

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

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

$$x=\sqrt{2}+1$$

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

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

The equation is now solved.

$$x=\sqrt{2}+1$$ $$x=-\sqrt{2}-1$$

Solve for x

$x=\sqrt{2}+1\approx 2.414213562$
$x=-\sqrt{2}-1\approx -2.414213562$