Solve Using the Square Root Property (6x-1)^2=-49

Solve Math

Algebra

${(6 x - 1)}^{2} = - 49$

Take the square root of each side of the equation to set up the solution for $x$

${(6 x - 1)}^{2 \cdot \frac{1}{2}} = \pm \sqrt{- 49}$

Remove the perfect root factor $6 x - 1$ under the radical to solve for $x$ .

$6 x - 1 = \pm \sqrt{- 49}$

Simplify the right side of the equation.

Tap for more steps...

Rewrite $- 49$ as $- 1 (49)$ .

$6 x - 1 = \pm \sqrt{- 1 \cdot 49}$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$6 x - 1 = \pm \sqrt{- 1} \cdot \sqrt{49}$

Rewrite $\sqrt{- 1}$ as $i$ .

$6 x - 1 = \pm i \cdot \sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$6 x - 1 = \pm i \cdot \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$6 x - 1 = \pm i \cdot 7$

Move $7$ to the left of $i$ .

$6 x - 1 = \pm 7 i$

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

Tap for more steps...

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

$6 x - 1 = 7 i$

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Add $1$ to both sides of the equation.

$6 x = 7 i + 1$

Reorder $7 i$ and $1$ .

$6 x = 1 + 7 i$

Divide each term by $6$ and simplify.

Tap for more steps...

Divide each term in $6 x = 1 + 7 i$ by $6$ .

$\frac{6 x}{6} = \frac{1}{6} + \frac{7 i}{6}$

Cancel the common factor of $6$ .

Tap for more steps...

Cancel the common factor.

$\frac{6 x}{6} = \frac{1}{6} + \frac{7 i}{6}$

Divide $x$ by $1$ .

$x = \frac{1}{6} + \frac{7 i}{6}$

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

$6 x - 1 = - 7 i$

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Add $1$ to both sides of the equation.

$6 x = - 7 i + 1$

Reorder $- 7 i$ and $1$ .

$6 x = 1 - 7 i$

Divide each term by $6$ and simplify.

Tap for more steps...

Divide each term in $6 x = 1 - 7 i$ by $6$ .

$\frac{6 x}{6} = \frac{1}{6} + \frac{- 7 i}{6}$

Cancel the common factor of $6$ .

Tap for more steps...

Cancel the common factor.

$\frac{6 x}{6} = \frac{1}{6} + \frac{- 7 i}{6}$

Divide $x$ by $1$ .

$x = \frac{1}{6} + \frac{- 7 i}{6}$

Move the negative in front of the fraction.

$x = \frac{1}{6} - \frac{7 i}{6}$

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

$x = \frac{1}{6} + \frac{7 i}{6}, \frac{1}{6} - \frac{7 i}{6}$

Do you know how to Solve Using the Square Root Property (6x-1)^2=-49? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	five hundred million two hundred sixty-seven thousand nine hundred ninety-four

Interesting facts

500267994 has 16 divisors, whose sum is 1010851968
The reverse of 500267994 is 499762005
Previous prime number is 97

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 42
Digital Root 6

Name

Name	six hundred forty-eight million four hundred thirty-four thousand two

Interesting facts

648434002 has 16 divisors, whose sum is 982420992
The reverse of 648434002 is 200434846
Previous prime number is 113

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 31
Digital Root 4

Name

Name	one billion four hundred forty-six million eight hundred eighty-two thousand two hundred eighty-six

Interesting facts

1446882286 has 16 divisors, whose sum is 2204296704
The reverse of 1446882286 is 6822886441
Previous prime number is 1823

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 49
Digital Root 4

Add (2-8i)+(5-i)

Evaluate 16*5

Factor y^2+7y-18

Find the Slope and Y-Intercept -12x+4y=-8

Find the Inverse y = log of x-8