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$-81$ x^ $2$ = $-11$ What are the solutions to the given equation?

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Find the missing exponent or base

Full solution

Q.

-81

x^

2

=

-11

What are the solutions to the given equation?

Divide by $-81$ : We are given the equation $-81x^2 = -11$ . To find the solutions for $x$ , we need to isolate $x$ by performing algebraic operations. The first step is to divide both sides of the equation by $-81$ to get $x^2$ by itself. $\newline$ Calculation: $x^2 = \frac{-11}{-81}$
Simplify right side: Simplify the right side of the equation by dividing $-11$ by $-81$ . $\newline$ Calculation: $x^2 = \frac{11}{81}$
Take square root: To find the value of $x$ , we need to take the square root of both sides of the equation. Since we are dealing with real numbers, we must consider both the positive and negative square roots. $\newline$ Calculation: $x = \pm\sqrt{\frac{11}{81}}$
Simplify square root: Simplify the square root of the fraction by taking the square root of the numerator and the denominator separately. $\newline$ Calculation: $x = \pm\sqrt{11} / \sqrt{81}$
Final simplification: Since the square root of $81$ is $9$ , we can further simplify the expression. $\newline$ Calculation: $x = \pm\sqrt{11} / 9$

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