Question
Use the quadratic formula to solve \( 2 x^{2}-4=0 \) \( x=\square \) Basic Funcs Trig
Ask by Hills O'Quinn. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = -\sqrt{2} \) or \( x = \sqrt{2} \)
Solution
Solve the equation \( 2x^2-4=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(2x^{2}-4=0\)
- step1: Add or subtract both sides:
\(2x^{2}=4\)
- step2: Divide both sides:
\(\frac{2x^{2}}{2}=\frac{4}{2}\)
- step3: Divide the numbers:
\(x^{2}=2\)
- step4: Simplify the expression:
\(x=\pm \sqrt{2}\)
- step5: Separate into possible cases:
\(\begin{align}&x=\sqrt{2}\\&x=-\sqrt{2}\end{align}\)
- step6: Rewrite:
\(x_{1}=-\sqrt{2},x_{2}=\sqrt{2}\)
The solutions to the equation \(2x^{2}-4=0\) are \(x=-\sqrt{2}\) and \(x=\sqrt{2}\).
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Simplify this solution Bonus Knowledge
To solve the equation \( 2x^2 - 4 = 0 \), we first rearrange it into standard form: \( 2x^2 = 4 \). Dividing both sides by 2 gives \( x^2 = 2 \). Taking the square root of both sides results in \( x = \pm\sqrt{2} \). Therefore, the solutions are \( x = \sqrt{2} \) and \( x = -\sqrt{2} \). Now, if we were to use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) with \( a = 2 \), \( b = 0 \), and \( c = -4 \), we’d compute it as follows: \( b^2 - 4ac = 0^2 - 4(2)(-4) = 32 \). Plugging it in gives \( x = \frac{0 \pm \sqrt{32}}{4} = \frac{\pm 4\sqrt{2}}{4} = \pm \sqrt{2} \), confirming our result.
