Solve the equation: x2 + 7x − 3 = 0

Mathematics

1 answer:

patriot [66]2 years ago

4 0

X = 1/2 ( If the 2 is not an exponent)
x = -7/2 ± √61/2 ( if 2 is the exponent)

Hoped I helped.

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$\bf \begin{array}{cccllll} \stackrel{\textit{point (0,-7)}}{-7=a(0)^2+b(0)+c}& \stackrel{point (7,-14)}{-14=a(7)^2+b(7)+c}& \stackrel{point (-3,-19)}{-19=a(-3)^2+b(-3)+c}\\\\ -7=c&-14=49a+7b+c&-19=9a-3b+c \end{array}$

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$\bf -14=49a+7b-7\implies -7=49a+7b\implies -7-49a=7b \\\\\\ \cfrac{-7-49a}{7}=b\implies \cfrac{-7}{7}-\cfrac{49a}{7}=b\implies -1-7a=b$

well, now let's plug that "b" into our 3rd equation and solve for "a".

$\bf -19=9a-3b-7\implies -12=9a-3b\implies -12=9a-3(-1-7a) \\\\\\ -12=9a+3+21a\implies -15=9a+21a\implies -15=30a \\\\\\ -\cfrac{15}{30}=a\implies \blacktriangleright -\cfrac{1}{2}=a \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{and since we know that}}{-1-7a=b}\implies -1-7\left( -\cfrac{1}{2} \right)=b\implies -1+\cfrac{7}{2}=b\implies \blacktriangleright \cfrac{5}{2}=b \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{2}x^2+\cfrac{5}{2}x-7~\hfill$

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Δx→0 −5(x + Δx) + 5x Δx

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1. The lowest common multiple between 15 and 12 is 60.
So, the new denominator of the fraction become 60.
2. Because 15*4= 60 ; 12*5 =60
For sustaining the balance, we should multiply 24 (the first molecule) to 4 times and multiply 12 (the second molecule) to 5 times.
Like, 24*4 and 32*5
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Thus, 256/60
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