Ingram Ford
10/02/2023 · Junior High School
2.Resolva as equações a seguir a) a) \( x^{2}-5 x+25=0 \)
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Step-by-step Solution
Solve the equation \( x^{2}-5x+25=0 \).
Solve the equation(The complex numbers system) by following steps:
- step0: Solve using the quadratic formula in the complex numbers system:
\(x^{2}-5x+25=0\)
- step1: Solve using the quadratic formula:
\(x=\frac{5\pm \sqrt{\left(-5\right)^{2}-4\times 25}}{2}\)
- step2: Simplify the expression:
\(x=\frac{5\pm \sqrt{-75}}{2}\)
- step3: Simplify the expression:
\(x=\frac{5\pm 5\sqrt{3}\times i}{2}\)
- step4: Separate into possible cases:
\(\begin{align}&x=\frac{5+5\sqrt{3}\times i}{2}\\&x=\frac{5-5\sqrt{3}\times i}{2}\end{align}\)
- step5: Simplify the expression:
\(\begin{align}&x=\frac{5}{2}+\frac{5\sqrt{3}}{2}i\\&x=\frac{5-5\sqrt{3}\times i}{2}\end{align}\)
- step6: Simplify the expression:
\(\begin{align}&x=\frac{5}{2}+\frac{5\sqrt{3}}{2}i\\&x=\frac{5}{2}-\frac{5\sqrt{3}}{2}i\end{align}\)
- step7: Rewrite:
\(x_{1}=\frac{5}{2}-\frac{5\sqrt{3}}{2}i,x_{2}=\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)
- step8: Remove the complex number(s):
\(\textrm{No real solution}\)
A equação \(x^{2}-5x+25=0\) não possui solução real.
Quick Answer
A equação \(x^{2}-5x+25=0\) não possui solução real.
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