cheshirecat23
Answered

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Consider the equation:
6x+55=x^2
1) Rewrite the equation by completing the square.
Your equation should look like (x+c)^2=d(x+c)
2
=dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(xβˆ’c)
2
=dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d.
2) What are the solutions to the equation?

Sagot :

Step-by-step explanation:

1.

Subtract the coefficient from both sides, keep 55 on the same side.

[tex] {x}^{2} - 6x = 55[/tex]

Complete the square by dividing the coefficient by two and squaring it.

[tex] {x}^{2} - 6x + 9 = 55 + 9[/tex]

Use binomial to factor the left side.

[tex](x - 3) {}^{2} = 64[/tex]

2. Solve for x.

[tex](x - 3) = 8[/tex]

[tex]x = 11[/tex]

Remeber the square root of 64 is also -8 so

[tex]x - 3 = - 8[/tex]

[tex]x = - 5[/tex]

So the solutions are -5 and 11

Answer:

Answers

1) We can rewrite the equation as 64=(xβˆ’3)^2

2) The solutions to the equation are x=3Β±8

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