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Solve
-48=(v-6)^(2), where
v is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".

Solve $-48=(v-6)^{2}$ , where $v$ is a real number. $\newline$ Round your answer to the nearest hundredth. $\newline$ If there is more than one solution, separate them with commas. $\newline$ If there is no solution, click on

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Conjugate root theorems

Full solution

Q. Solve

-48=(v-6)^{2}

, where

v

is a real number.

\newline

Round your answer to the nearest hundredth.

\newline

If there is more than one solution, separate them with commas.

\newline

If there is no solution, click on

Take Square Root: Now, take the square root of both sides to solve for $v - 6$ . Remember, there are two solutions when taking the square root, one positive and one negative. $v - 6 = \pm\sqrt{48}$
Simplify Square Root: Simplify the square root of $48$ . $\sqrt{48} = \sqrt{(16 \times 3)} = 4\sqrt{3}$ So, $v - 6 = \pm 4\sqrt{3}$
Add $6$ : Add $6$ to both sides to solve for $v$ . $\newline$ $v = 6 \pm 4\sqrt{3}$
Calculate Approximate Values: Now, let's calculate the approximate values of $v$ . $v \approx 6 + 4\sqrt{3}$ and $v \approx 6 - 4\sqrt{3}$ $v \approx 6 + 4(1.73)$ and $v \approx 6 - 4(1.73)$ $v \approx 6 + 6.92$ and $v \approx 6 - 6.92$ $v \approx 12.92$ and $v \approx -0.92$ Round to the nearest hundredth. $v \approx 12.92$ and $v \approx -0.92$

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