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How many distinct real solutions does the given equation have? $1{,}000=20z^2$

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Domain and range of quadratic functions: equations

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Q. How many distinct real solutions does the given equation have?

1{,}000=20z^2

Write Equation: First, let's write down the equation we need to solve: $1{,}000 = 20z^2$ . $\newline$ We want to find the number of distinct real solutions for $z$ .
Isolate z^ $2$ : To solve for $z$ , we need to isolate $z^2$ by dividing both sides of the equation by $20$ . $\newline$ $\frac{1{,}000}{20} = \frac{20z^2}{20}$ $\newline$ $50 = z^2$
Take Square Root: Now we take the square root of both sides to solve for $z$ . $\newline$ $\sqrt{50} = \sqrt{z^2}$ $\newline$ This gives us two possible solutions for $z$ : $z = \sqrt{50}$ or $z = -\sqrt{50}$ .
Find Real Solutions: Since $\sqrt{50}$ is a real number, both $\sqrt{50}$ and $-\sqrt{50}$ are real numbers. $\newline$ Therefore, the equation has two distinct real solutions.

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