How to solve 7(x)^(2)=(1)/(28)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 7(x)^(2)=(1)/(28) | Equatix

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Question

$$7 { x }^{ 2 } = \frac{ 1 }{ 28 }$$

Solve for x

$x=\frac{1}{14}\approx 0.071428571$
$x=-\frac{1}{14}\approx -0.071428571$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Divide both sides by $7$.

$$x^{2}=\frac{\frac{1}{28}}{7}$$

Express $\frac{\frac{1}{28}}{7}$ as a single fraction.

$$x^{2}=\frac{1}{28\times 7}$$

Multiply $28$ and $7$ to get $196$.

$$x^{2}=\frac{1}{196}$$

Subtract $\frac{1}{196}$ from both sides.

$$x^{2}-\frac{1}{196}=0$$

Multiply both sides by $196$.

$$196x^{2}-1=0$$

Consider $196x^{2}-1$. Rewrite $196x^{2}-1$ as $\left(14x\right)^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(14x-1\right)\left(14x+1\right)=0$$

To find equation solutions, solve $14x-1=0$ and $14x+1=0$.

$$x=\frac{1}{14}$$ $$x=-\frac{1}{14}$$

Steps by Finding Square Root

Divide both sides by $7$.

$$x^{2}=\frac{\frac{1}{28}}{7}$$

Express $\frac{\frac{1}{28}}{7}$ as a single fraction.

$$x^{2}=\frac{1}{28\times 7}$$

Multiply $28$ and $7$ to get $196$.

$$x^{2}=\frac{1}{196}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{14}$$ $$x=-\frac{1}{14}$$

Steps Using the Quadratic Formula

Divide both sides by $7$.

$$x^{2}=\frac{\frac{1}{28}}{7}$$

Express $\frac{\frac{1}{28}}{7}$ as a single fraction.

$$x^{2}=\frac{1}{28\times 7}$$

Multiply $28$ and $7$ to get $196$.

$$x^{2}=\frac{1}{196}$$

Subtract $\frac{1}{196}$ from both sides.

$$x^{2}-\frac{1}{196}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-\frac{1}{196}$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{196}\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{196}\right)}}{2}$$

Multiply $-4$ times $-\frac{1}{196}$.

$$x=\frac{0±\sqrt{\frac{1}{49}}}{2}$$

Take the square root of $\frac{1}{49}$.

$$x=\frac{0±\frac{1}{7}}{2}$$

Now solve the equation $x=\frac{0±\frac{1}{7}}{2}$ when $±$ is plus.

$$x=\frac{1}{14}$$

Now solve the equation $x=\frac{0±\frac{1}{7}}{2}$ when $±$ is minus.

$$x=-\frac{1}{14}$$

The equation is now solved.

$$x=\frac{1}{14}$$ $$x=-\frac{1}{14}$$

Show Solution

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Example

Question

Solve for x

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula