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Afina-wow [57]
3 years ago
7

X^(2) + 10x=24 by completeing the square

Mathematics
1 answer:
melisa1 [442]3 years ago
4 0
(b/2)^2=(−5)^2
x^2−10x+(−5)^2=<span>24+<span>(−5)^<span>2
</span></span></span><span><span>x^2−10x+25</span>=49
</span><span><span>(x−5)^</span>2</span>=<span>49 (square root)
</span><span>(<span>x<span>−5</span></span>)</span>=<span>±<span>7

x-5=7 => x=12 
x-5=-7 => x=-2</span></span>
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x+3y=12

Step-by-step explanation:

Given:

x-intercept = 12

y-intercept = 4

To find the equation of line in the form ax+by=c where a,b,c  are integers with no factor common to all​ three, and greater than or equal 0.

Solution:

The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as (x,0)

Thus, on point of the line is (12,0)

The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as (0,y).

Thus, on point of the line is (0,4)

Using the two points we can find the slope of the line using the slope formula.

m=\frac{y_2-y_1}{x_2-x_1}

So, slope of the line can b given as:

m=\frac{4-0}{0-12}

m=\frac{4}{-12}

m=-\frac{1}{3}

The slope intercept form of the equation of he line is given as:

y=mx+b

where m represents slope of the line and b represents the y-intercept.

So, the equation of the line can be given as:

y=-\frac{1}{3}x+4

Multiplying each term by 3 to remove fraction.

3y=3.-\frac{1}{3}x+4(3)

3y=-x+12

Adding x both sides.

3y+x=-x+x+12

3y+x=12

Thus, the equation of the line  in ax+by=c  form where a,b,c  are integers with no factor common to all​ three, and greater than or equal 0 is:

x+3y=12

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