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Help Spock solve and simplify \[ x^{2}=180 \]

Ask by Barnett Barnett. in the United States
Feb 21,2025

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The solutions are \( x = -6\sqrt{5} \) and \( x = 6\sqrt{5} \).

Solución

Solve the equation \( x^{2}=180 \). Solve the quadratic equation by following steps: - step0: Solve using square roots: \(x^{2}=180\) - step1: Simplify the expression: \(x=\pm \sqrt{180}\) - step2: Simplify the expression: \(x=\pm 6\sqrt{5}\) - step3: Separate into possible cases: \(\begin{align}&x=6\sqrt{5}\\&x=-6\sqrt{5}\end{align}\) - step4: Rewrite: \(x_{1}=-6\sqrt{5},x_{2}=6\sqrt{5}\) The solutions to the equation \(x^{2}=180\) are \(x=-6\sqrt{5}\) and \(x=6\sqrt{5}\).

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The Deep Dive

To solve for \( x \), start by taking the square root of both sides. This gives us: \[ x = \sqrt{180} \] Now, we can simplify \( \sqrt{180} \). Notice that \( 180 = 36 \times 5 \), and since 36 is a perfect square, we have: \[ x = \sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5} \] So, the simplified solution is: \[ x = 6\sqrt{5} \]

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