quadratic equation: solve by completing: x^2 + 10x + 13 = 0?

Answer 1

x² + 10x + 13 = 0

x² + 10x = -25

x² + (2*5) x + 25 = -13 + 25

(x + 5)² = 12

(x + 5) = ±√12

x = -5 ± 2√3

Answer 2

x^2 + 10x + 13 = 0

In order to complete the square, what you have to do is add the proper number in order to make a square binomial. To get this number, you need to take "half squared" of the coefficient of x. So you want half-squared of 10.

When I say "half squared", (1) Multiply 10 by 1/2, and then (2) square the result.
10 * (1/2) = 10/2 = 5, squared is 25.

So our magic number is 25.

Now, we insert this 25 in between the 10x and 13.

x^2 + 10x + 25 + 13 + ? = 0

I put a question mark there because you can't just add something to an equation and leave it at that; you have to offset the number you just added. In this case, you have to offset the +25 by subtracting 25. Therefore,

x^2 + 10x + 25 + 13 - 25 = 0

Now, the first three terms form a perfect binomial square, and can be written as follows.

(x + 5)^2 + 13 - 25 = 0

Combine the 13 and -25, to get

(x + 5)^2 - 12 = 0

Bring the -12 over, to get

(x + 5)^2 = 12

Now, take the square root of both sides. Keep in mind that in doing so, you have to insert a "plus or minus" symbol in front of the right hand side; that is "+/-" (on paper, it looks like a plus sign on top of a minus sign).

Note that when taking the square root of the left hand side, it eliminates the power of 2.

x + 5 = +/- sqrt(12)

sqrt(12) can be reduced to 2sqrt(3), so we have

x + 5 = +/- 2sqrt(3)

Now, move the +5 to the other side, to get

x = -5 +/- 2sqrt(3)

So your two values for x are
x = {-5 + 2sqrt(3) , -5 - 2sqrt(3)}

Answer 3

The first step is to subtract 13 from both sides:
x^2+10x=-13

Take the 10 and divide it by two and then square the answer after that:
10/2=5
5^2=25

x^2+10x+25=-13
x^2+10x+25=-13+25
x^2+10x+25=12
(x+5)^2=12
√(x+5)^2=√12
x+5=√12
x=-5±√12
x=-5±2√3

Answer 4

x² + 10x + 13 = 0

x² + 10X + 13 - 13 = 0 - 13

x² + 10x = - 13

x² + 10x + 25 = - 13 + 25

x² + 10x + 25 = 12

(x + 5)(x + 5) = 12

(x + 5)² = √12

x + 5 = √4 √3

x + 5 = 2√3

x + 5 - 5 = - 5 ± 2√3

x = - 5 ± 2√3

- - - - - - - -s-

Answer 5

Your chum is ideal 6x^2 - 2x = 0 x is a elementary element, so take an x out x(6x - 2) = 0 Now, set both factors equivalent to 0 x = 0 6x - 2 = 0 make certain for x x = 0 6x - 2 = 0 6x = 2 x = 2/6 x = a million/3 The x-intercepts will be 0 and a million/3, like your chum reported. EDIT: definite, you're good, a is 6 and b is -2, basically change x = -b/2a x = -(-2)/2(6) x = 4/12 x = a million/3, that is the x-coordinate of the vertex Now, change this into the equation to locate the y-coordinate. 6x^2 - 2x = y 6(a million/3)^2 - 2(a million/3) = y 6(a million/9) - (2/3) = y 2/3 - 2/3 = y 0 = y, the y-coordinate is 0 hence, the vertex is (a million/3 , 0)

Answer 6

use half formula

a=1
b=10
b/2=5
c=13

x=-5 + or - sqrt(25-13) /1 =

x=-5 + or - sqrt(12)
two distinct roots

Answer 7

x = -1.5359 or -8.4641

memorize the quadratic formula!!!!