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Sagot :
Para despejar [tex]\( x \)[/tex] de la ecuación [tex]\( a - c \sqrt{x + m} = b \)[/tex], vamos a seguir estos pasos:
1. Aislar el término con la raíz cuadrada:
[tex]\[ a - b = c \sqrt{x + m} \][/tex]
restando [tex]\( b \)[/tex] de ambos lados de la ecuación obtienes:
[tex]\[ a - b = c \sqrt{x + m} \][/tex]
2. Dividir ambos lados de la ecuación por [tex]\( c \)[/tex]:
[tex]\[ \frac{a - b}{c} = \sqrt{x + m} \][/tex]
3. Elevar ambos lados al cuadrado para eliminar la raíz cuadrada:
[tex]\[ \left( \frac{a - b}{c} \right)^2 = x + m \][/tex]
4. Restar [tex]\( m \)[/tex] de ambos lados para aislar [tex]\( x \)[/tex]:
[tex]\[ x = \left( \frac{a - b}{c} \right)^2 - m \][/tex]
Por lo tanto, [tex]\( x \)[/tex] despejado es:
[tex]\[ x = \left( \frac{a - b}{c} \right)^2 - m \][/tex]
1. Aislar el término con la raíz cuadrada:
[tex]\[ a - b = c \sqrt{x + m} \][/tex]
restando [tex]\( b \)[/tex] de ambos lados de la ecuación obtienes:
[tex]\[ a - b = c \sqrt{x + m} \][/tex]
2. Dividir ambos lados de la ecuación por [tex]\( c \)[/tex]:
[tex]\[ \frac{a - b}{c} = \sqrt{x + m} \][/tex]
3. Elevar ambos lados al cuadrado para eliminar la raíz cuadrada:
[tex]\[ \left( \frac{a - b}{c} \right)^2 = x + m \][/tex]
4. Restar [tex]\( m \)[/tex] de ambos lados para aislar [tex]\( x \)[/tex]:
[tex]\[ x = \left( \frac{a - b}{c} \right)^2 - m \][/tex]
Por lo tanto, [tex]\( x \)[/tex] despejado es:
[tex]\[ x = \left( \frac{a - b}{c} \right)^2 - m \][/tex]
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