Stanley Gough
07/08/2024 · Junior High School
Solve \( 5 x^{2}+35=0 \)
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Step-by-step Solution
Solve the equation \( 5x^{2}+35=0 \).
Solve the equation(The complex numbers system) by following steps:
- step0: Solve using square roots:
\(5x^{2}+35=0\)
- step1: Add or subtract both sides:
\(5x^{2}=-35\)
- step2: Divide both sides:
\(\frac{5x^{2}}{5}=\frac{-35}{5}\)
- step3: Divide the numbers:
\(x^{2}=-7\)
- step4: Simplify the expression:
\(x=\pm \sqrt{-7}\)
- step5: Simplify the expression:
\(x=\pm \left(\sqrt{7}\times i\right)\)
- step6: Separate into possible cases:
\(\begin{align}&x=\sqrt{7}\times i\\&x=-\sqrt{7}\times i\end{align}\)
- step7: Rewrite:
\(x_{1}=-\sqrt{7}\times i,x_{2}=\sqrt{7}\times i\)
- step8: Remove the complex number(s):
\(\textrm{No real solution}\)
The equation \(5x^{2}+35=0\) has no real solutions.
Quick Answer
The equation has no real solutions.
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