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equacar do \( 2 x^{2}-14 x+20=0 \)

Ask by Potter Bond. in Angola
Feb 20,2025

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As soluções da equação \( 2x^{2}-14x+20=0 \) são \( x = 2 \) e \( x = 5 \).

Solución

Solve the quadratic equation by following steps: - step0: Solve by factoring: \(2x^{2}-14x+20=0\) - step1: Factor the expression: \(2\left(x-5\right)\left(x-2\right)=0\) - step2: Divide the terms: \(\left(x-5\right)\left(x-2\right)=0\) - step3: Separate into possible cases: \(\begin{align}&x-5=0\\&x-2=0\end{align}\) - step4: Solve the equation: \(\begin{align}&x=5\\&x=2\end{align}\) - step5: Rewrite: \(x_{1}=2,x_{2}=5\) Para resolver a equação \( 2x^{2}-14x+20=0 \), encontramos as raízes: As soluções são: - \( x_{1} = 2 \) - \( x_{2} = 5 \) Portanto, as raízes da equação são \( x = 2 \) e \( x = 5 \).

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The Deep Dive

Para resolver a equação \( 2x^{2} - 14x + 20 = 0 \), você pode começar dividindo todos os termos por 2 para simplificar a equação: \( x^{2} - 7x + 10 = 0 \). A seguir, você pode fatorar a expressão, encontrando números que somados dão -7 e multiplicados dão 10. Esses números são -5 e -2, então a equação fatorada é \( (x - 5)(x - 2) = 0 \). Assim, as soluções são \( x = 5 \) e \( x = 2 \). Esse tipo de equação é bastante comum em problemas de física e engenharia, especialmente na determinação de trajetórias ou otimizações. Sabendo que muitas vezes estamos lidando com movimentos, estabelecer as raízes da equação pode nos ajudar a descobrir em que pontos um objeto atinge certas alturas ou distâncias, sendo uma ferramenta frequentemente usada em cenários práticos.

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