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2. Consider the equation x2 + 8x = 10.

(a) Show how to solve the equation by completing the square.
(b) Show how to solve the equation by using the quadratic formula. Round solutions to the nearest tenth if needed.

1 Answer

4 votes

ANSWER

x=1.1 or x=-9.1

Step-by-step explanation


{x}^(2) + 8x = 10

Ad the square of half the coefficient of x to both sides:


{x}^(2) + 8x + {4}^(2) = 10 + {4}^(2)


{x}^(2) + 8x + 16= 10 + 16

The left hand side is now a perfect square.


{(x + 4)}^(2) = 26

Take square root


x + 4= \pm √(26)


x = - 4 \pm √(26)

x=1.1 or x=-9.1

Using the quadratic formula, we need to rewrite the given equation to get;


{x}^(2) + 8x - 10 = 0

where a=1, b=8 and c=-10

The solution is given by:


x = \frac{ - b \pm \: \sqrt{ {b}^(2) - 4ac } }{2a}

We substitute the values into the formula to get;


x = \frac{ - 8\pm \: \sqrt{ {8}^(2) - 4(1)( - 10) } }{2(1)}


x = ( - 8\pm \: √( 104 ) )/(2)


x = ( - 8\pm \: 2√( 26 ) )/(2)


x = - 4\pm \: √( 26 )

x=1.1 or x=-9.1

to the nearest tenth.

User Nietras
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