Solve Using the Square Root Property -5x^2=11

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Algebra

$- 5 x^{2} = 11$

Divide each term by $- 5$ and simplify.

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Divide each term in $- 5 x^{2} = 11$ by $- 5$ .

$\frac{- 5 x^{2}}{- 5} = \frac{11}{- 5}$

Cancel the common factor of $- 5$ .

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Cancel the common factor.

$\frac{- 5 x^{2}}{- 5} = \frac{11}{- 5}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{11}{- 5}$

Move the negative in front of the fraction.

$x^{2} = - \frac{11}{5}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- \frac{11}{5}}$

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite $- 1$ as $i^{2}$ .

$x = \pm \sqrt{i^{2} (\frac{11}{5})}$

Pull terms out from under the radical.

$x = \pm i \sqrt{\frac{11}{5}}$

Rewrite $\sqrt{\frac{11}{5}}$ as $\frac{\sqrt{11}}{\sqrt{5}}$ .

$x = \pm i (\frac{\sqrt{11}}{\sqrt{5}})$

Multiply $\frac{\sqrt{11}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$x = \pm i (\frac{\sqrt{11}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}})$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{11}}{\sqrt{5}}$ and $\frac{\sqrt{5}}{\sqrt{5}}$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{\sqrt{5} \sqrt{5}})$

Raise $\sqrt{5}$ to the power of $1$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{\sqrt{5} \sqrt{5}})$

Raise $\sqrt{5}$ to the power of $1$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{\sqrt{5} \sqrt{5}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{{\sqrt{5}}^{1 + 1}})$

Add $1$ and $1$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{{\sqrt{5}}^{2}})$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}})$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}})$

Combine $\frac{1}{2}$ and $2$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{5^{\frac{2}{2}}})$

Cancel the common factor of $2$ .

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Cancel the common factor.

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{5^{\frac{2}{2}}})$

Divide $1$ by $1$ .

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{5})$

Evaluate the exponent.

$x = \pm i (\frac{\sqrt{11} \sqrt{5}}{5})$

Simplify the numerator.

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Combine using the product rule for radicals.

$x = \pm i (\frac{\sqrt{11 \cdot 5}}{5})$

Multiply $11$ by $5$ .

$x = \pm i (\frac{\sqrt{55}}{5})$

Combine $i$ and $\frac{\sqrt{55}}{5}$ .

$x = \pm \frac{i \sqrt{55}}{5}$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$x = \frac{i \sqrt{55}}{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{i \sqrt{55}}{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{i \sqrt{55}}{5}, - \frac{i \sqrt{55}}{5}$

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Name

Name	one billion three hundred twenty-four million one hundred twenty-eight thousand seven hundred seventy-seven

Interesting facts

1324128777 has 8 divisors, whose sum is 1826384640
The reverse of 1324128777 is 7778214231
Previous prime number is 29

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 42
Digital Root 6

Name

Name	seven hundred seventy million forty-one thousand eight hundred seventeen

Interesting facts

770041817 has 8 divisors, whose sum is 825239616
The reverse of 770041817 is 718140077
Previous prime number is 37

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 35
Digital Root 8

Name

Name	one billion five hundred fifty-six million six hundred seventy-four thousand nine hundred forty-six

Interesting facts

1556674946 has 8 divisors, whose sum is 2338590204
The reverse of 1556674946 is 6494766551
Previous prime number is 653

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 53
Digital Root 8

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