Mathematics, 09.07.2019 17:00 xdimplesjoon

2x^2+4x+1 the quadratic and completing the square

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Quadratic Formula:
Solve for x over the real numbers:2 x^2 + 4 x + 1 = 0
x = (-4 ± sqrt(4^2 - 4×2))/(2×2) = (-4 ± sqrt(16 - 8))/4 = (-4 ± sqrt(8))/4:x = (-4 + sqrt(8))/4 or x = (-4 - sqrt(8))/4
sqrt(8) = sqrt(2^3) = 2sqrt(2):x = (-4 + 2 sqrt(2))/4 or x = (-4 - 2 sqrt(2))/4
Factor 2 from -4 + 2 sqrt(2) giving 2 (sqrt(2) - 2):x = (2 (sqrt(2) - 2))/4 or x = (-2 sqrt(2) - 4)/(4)
(2 (sqrt(2) - 2))/4 = (2 (sqrt(2) - 2))/(2×2) = (sqrt(2) - 2)/2:x = (sqrt(2) - 2)/2 or x = (-2 sqrt(2) - 4)/(4)
Factor 2 from -4 - 2 sqrt(2) giving 2 (-sqrt(2) - 2):x = 1/2 (sqrt(2) - 2) or x = (2 (-sqrt(2) - 2))/4
(2 (-sqrt(2) - 2))/4 = (2 (-sqrt(2) - 2))/(2×2) = (-sqrt(2) - 2)/2: x = 1/2 (sqrt(2) - 2) or x = (-sqrt(2) - 2)/2

Complete the Square:
Solve for x over the real numbers:2 x^2 + 4 x + 1 = 0
Divide both sides by 2:x^2 + 2 x + 1/2 = 0
Subtract 1/2 from both sides:x^2 + 2 x = -1/2
Add 1 to both sides:x^2 + 2 x + 1 = 1/2
Write the left-hand side as a square:(x + 1)^2 = 1/2
Take the square root of both sides:x + 1 = 1/sqrt(2) or x + 1 = -1/sqrt(2)
Subtract 1 from both sides:x = 1/sqrt(2) - 1 or x + 1 = -1/sqrt(2)
Subtract 1 from both sides: x = 1/sqrt(2) - 1 or x = -1 - 1/sqrt(2)

Answer from: Quest

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

Answer from: Quest

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

$x^2-2x+y^2-6y=26$

we now create space between the x and y terms with parenthesis.

$(x^2-2x)+(y^2-6y)=26$

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

$\frac{-2}{2} =(-1)^{2} =1$

$\frac{-6}{2} =(-3)^{2} =9$

we add the squares to both sides.

$(x^2-2x+1)+(y^2-6y+9)=26+1+9$

simplify.

$(x^2-2x+1)+(y^2-6y+9)=36$

and write the quadratics in factored form.

$(x-1)^{2} +(y-3)^{2} =36$

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

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