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3 years ago

Solve 3x2 + 18x + 15 = 0 by completing the square.

1 answer:

3 0

3x^2 + 18x + 15 = 0
15 + 18x + 3x2 = 0
3(5 + 6x + x2) = 0
3((5 + x)(1 + x)) = 0
5 + x = 0
5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5
x = -5
--------------------------------------------
1 + x = 0 x=-1
-5,-1

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Answer:

$(2,\, 6)$ .

Step-by-step explanation:

Let $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$ denote the two endpoints.

The formula for the midpoint of these two points would be:

$\displaystyle \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)$ .

(Similar to taking the average of each coordinate.)

In this question, it is given that $x_{0} = 10$ whereas $y_{0} = 12$ . Substitute these two values into the expression for the coordinate of the midpoint:

$x$ -coordinate of the midpoint: $\displaystyle \frac{10 + x_{1}}{2} = 6$ .
$y$ -coordinate of the midpoint: $\displaystyle \frac{12 + y_{1}}{2} = 9$ .

Solve these two equations for $x_{1}$ and $y_{1}$ : $x_{1} = 2$ whereas $y_{1} = 6$ .

Hence, the coordinate of the other point would be $(2,\, 6)$ .

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2 years ago

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maxonik [38]

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