Solve 100(x)^(2)-20\times+1=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

$$100 { x }^{ 2 } -20 \times +1=0$$

Solve for x

$x=\frac{\sqrt{5}}{5}\approx 0.447213595$
$x=-\frac{\sqrt{5}}{5}\approx -0.447213595$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply $20$ and $1$ to get $20$.

$$100x^{2}-20=0$$

Add $20$ to both sides. Anything plus zero gives itself.

$$100x^{2}=20$$

Divide both sides by $100$.

$$x^{2}=\frac{20}{100}$$

Reduce the fraction $\frac{20}{100}$ to lowest terms by extracting and canceling out $20$.

$$x^{2}=\frac{1}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{5}}{5}$$ $$x=-\frac{\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Multiply $20$ and $1$ to get $20$.

$$100x^{2}-20=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $100$ for $a$, $0$ for $b$, and $-20$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-20\right)}}{2\times 100}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 100\left(-20\right)}}{2\times 100}$$

Multiply $-4$ times $100$.

$$x=\frac{0±\sqrt{-400\left(-20\right)}}{2\times 100}$$

Multiply $-400$ times $-20$.

$$x=\frac{0±\sqrt{8000}}{2\times 100}$$

Take the square root of $8000$.

$$x=\frac{0±40\sqrt{5}}{2\times 100}$$

Multiply $2$ times $100$.

$$x=\frac{0±40\sqrt{5}}{200}$$

Now solve the equation $x=\frac{0±40\sqrt{5}}{200}$ when $±$ is plus.

$$x=\frac{\sqrt{5}}{5}$$

Now solve the equation $x=\frac{0±40\sqrt{5}}{200}$ when $±$ is minus.

$$x=-\frac{\sqrt{5}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{5}}{5}$$ $$x=-\frac{\sqrt{5}}{5}$$