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expeople1 [14]
3 years ago
14

Solve the quadratic equation by completing the square. x^2+12x+52=0

Mathematics
1 answer:
White raven [17]3 years ago
6 0

Answer:

(x + 6)² + 16 = 0

Step-by-step explanation:

To complete the square we will first need to get our equation to look like: x² + bx = c

Here we have x² + bx + c = 0 → x² + 12x + 52 = 0

  • First we need to subtract our c, in this case 52, from both sides to get x² + 12x = -52
  • We then need to add (\frac{b}{2} )^{2} to both sides of the equation
  • Here our b value is 12, so plugging this into our formula we get (\frac{12}{2} )^{2} =(6)^{2} =36
  • Adding 36 to both sides our equation becomes: x² + 12x + 36 = -52 + 36
  • Then combining like terms on the right side we get x² + 12x + 36 = -16
  • Now making our left side of the equation into a perfect square we get: (x + 6)² = -16
  • Finally adding the 16 to both sides of the equation we get: (x + 6)² + 16 = 0

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Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

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Further simplification gives us

3a= a/(1-r)

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3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

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= 3r= 2

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= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

5 0
3 years ago
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Answer:

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Step-by-step explanation:

-6(2+(6)=-48

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Step-by-step explanation: Hope this helps!

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Answer:

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