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07/08/2023 · High School
b) \( x^{2}+8 x+3=0 \)
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Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( x^{2}+8x+3=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
\(x^{2}+8x+3=0\)
- step1: Solve using the quadratic formula:
\(x=\frac{-8\pm \sqrt{8^{2}-4\times 3}}{2}\)
- step2: Simplify the expression:
\(x=\frac{-8\pm \sqrt{52}}{2}\)
- step3: Simplify the expression:
\(x=\frac{-8\pm 2\sqrt{13}}{2}\)
- step4: Separate into possible cases:
\(\begin{align}&x=\frac{-8+2\sqrt{13}}{2}\\&x=\frac{-8-2\sqrt{13}}{2}\end{align}\)
- step5: Simplify the expression:
\(\begin{align}&x=-4+\sqrt{13}\\&x=\frac{-8-2\sqrt{13}}{2}\end{align}\)
- step6: Simplify the expression:
\(\begin{align}&x=-4+\sqrt{13}\\&x=-4-\sqrt{13}\end{align}\)
- step7: Rewrite:
\(x_{1}=-4-\sqrt{13},x_{2}=-4+\sqrt{13}\)
La solución de la ecuación \(x^{2}+8x+3=0\) es \(x_{1}=-4-\sqrt{13}\) y \(x_{2}=-4+\sqrt{13}\).
Quick Answer
La solución de la ecuación es \(x_{1}=-4-\sqrt{13}\) y \(x_{2}=-4+\sqrt{13}\).
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