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nordsb [41]
3 years ago
12

Elise has to use the information given below to find the original number. Write an equation to represent the situation. What is

the original​ number?
If you double a number and then add 24​, you get two sevenths27 of the original number.
Mathematics
1 answer:
lilavasa [31]3 years ago
3 0
Let x= original number
equation: 2x+24=2/7 x
move 2x over to the other side of the equation to get 24=-12/7 x. Then, multiply both sides of the equation by -7/12 to isolate the variable.
The final answer should be x=-14
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Verdich [7]

Answer:

x=-1,\:x=-7,\:x=i,\:x=-i

Step-by-step explanation:

Considering the equation

x^4+8x^3+8x^2+8x+7=0

Solving

x^4+8x^3+8x^2+8x+7

\mathrm{Factor\:}x^4+8x^3+8x^2+8x+7:\quad \left(x+1\right)\left(x+7\right)\left(x^2+1\right)

As

\mathrm{Use\:the\:rational\:root\:theorem}

a_0=7,\:\quad a_n=1

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\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:7}{1}

-\frac{1}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+1

=\left(x+1\right)\frac{x^4+8x^3+8x^2+8x+7}{x+1}...[A]

Solving

\frac{x^4+8x^3+8x^2+8x+7}{x+1}

=x^3+7x^2+x+7

Putting \frac{x^4+8x^3+8x^2+8x+7}{x+1} =  x^3+7x^2+x+7 in equation [A]

So,

\left(x+1\right)\frac{x^4+8x^3+8x^2+8x+7}{x+1}...[A]

=\left(x+1\right)x^3+7x^2+x+7

As

x^3+7x^2+x+7=\left(x+7\right)\left(x^2+1\right)

So,

Equation [A] becomes

=\left(x+1\right)\left(x+7\right)\left(x^2+1\right)

So,  the polynomial equation becomes

\left(x+1\right)\left(x+7\right)\left(x^2+1\right)=0

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\mathrm{Solve\:}\:x+7=0:\quad x=-7

\mathrm{Solve\:}\:x^2+1=0:\quad x=i,\:x=-i

\mathrm{The\:solutions\:are}

x=-1,\:x=-7,\:x=i,\:x=-i

Keywords: polynomial equation

Learn polynomial equation from brainly.com/question/12240569

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