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Answer
Las soluciones son \(x = -1.8\) y \(x = -1\).
Solution
Solve the equation \( 5x^2+14x+9=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(5x^{2}+14x+9=0\)
- step1: Factor the expression:
\(\left(x+1\right)\left(5x+9\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x+1=0\\&5x+9=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=-1\\&x=-\frac{9}{5}\end{align}\)
- step4: Rewrite:
\(x_{1}=-\frac{9}{5},x_{2}=-1\)
La solución de la ecuación \(5x^2+14x+9=0\) es \(x_{1}=-\frac{9}{5}\) y \(x_{2}=-1\), o en forma decimal, \(x_{1}=-1.8\) y \(x_{2}=-1\).
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Simplify this solution Beyond the Answer
To solve the quadratic equation \( 5x^2 + 14x + 9 = 0 \), you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). In this equation, \( a = 5 \), \( b = 14 \), and \( c = 9 \). Plug these values into the formula to find the roots. The discriminant is \( b^2 - 4ac = 14^2 - 4(5)(9) = 196 - 180 = 16 \). Since the discriminant is positive, there are two distinct real roots. Calculate \( x \) using the quadratic formula to find the solutions. By simplifying, you’ll find that \( x = \frac{-14 \pm 4}{10} \), which leads you to the two solutions: \( x = -1 \) and \( x = -\frac{9}{5} \). Happy calculating!
