Select the correct answer. What is the solution to the equation? $$ -2 \sqrt{x}+4=-12 $$ A. 4 B. 8 C. 16 D. 64

1. Start with the equation: \[ -2 \sqrt{x} + 4 = -12 \] 2. Subtract 4 from both sides to isolate the term with $$\sqrt{x}$$: \[ -2 \sqrt{x} = -12 - 4 = -16 \] 3. Divide both sides by $$-2$$ to solve for $$\sqrt{x}$$: \[ \sqrt{x} = \frac{-16}{-2} = 8 \] 4. Square both sides to solve for $$x$$: \[ x = 8^2 = 64 \] The correct answer is D. The solution is $$ x = 64 $$, which is option D.

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Pregunta

Select the correct answer.
What is the solution to the equation?

A. 4
B. 8
C. 16
D. 64

Ask by Wyatt Harmon. in the United States

Mar 31,2025

Solución de inteligencia artificial de Upstudy

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Responder

The solution is

, which is option D.

Solución

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Como

The Deep Dive

To solve the equation

, we start by isolating the square root. Subtract 4 from both sides to get

. Next, divide both sides by -2, yielding

. Now, to find

, we square both sides, resulting in

. Therefore, the correct answer is D. 64.

Did you know that the concept of square roots dates back thousands of years? Ancient Babylonians were already utilizing geometric methods to solve quadratic equations around 2000 BC! They had a good understanding of these concepts long before algebra became a formal branch of mathematics.

If you’re ever unsure while solving equations, it’s easy to make mistakes with signs or operations. A great tip is to double-check each step. For instance, always verify that you’ve isolated the variable before squaring, as doing things out of order can lead you down the wrong path. Happy solving!

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