anonymous
  • anonymous
desperate need of help Using the factoring process, what constant is added to the RIGHT side of the quadratic equation 2x2 + 8x + ___ = 15 + ___ in order to solve by completing the square?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
its 4 isnt it
anonymous
  • anonymous
2x2− 5x + ___ = 12 + ___
mathstudent55
  • mathstudent55
In order to complete a square, you need to have a coefficient of 1 for the x^2 term. We can factor out a 2. \(2x^2 + 8x + \_\_\_ = 15 + \_\_\_ \) \(2(x^2 + 4x + \_\_\_) = 15 + \_\_\_\) Now to complete the square, take half of the middle term coefficient and square it. The middle-term coefficient is 4. Take half of that and square it. What do you get?

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anonymous
  • anonymous
4
anonymous
  • anonymous
i need help with this one too 2x2− 5x + ___ = 12 + ___ i can't do fractions
anonymous
  • anonymous
i can post in as a new question so you can have two medals
mathstudent55
  • mathstudent55
Good. Now we place a 4 in the first blank. \(\color{green}{2}(x^2 + 4x + \color{red}{4}) = 15 + \_\_\_\) Notice the factor of 2 outside the parentheses. This means that the 4 after multiplying by 2 is really 8 that you are adding to the left side, so you need to add 8 to the right side. \(\color{green}{2}(x^2 + 4x + \color{red}{4}) = 15 + \color{red}{8}\)
mathstudent55
  • mathstudent55
With your second problem, again, you need to factor out a 2 from the left side, so you have plain x^2, not 2x^2. \(2x^2− 5x + \_\_\_ = 12 + \_\_\_ \) \(2(x^2− \dfrac{5}{2}x + \_\_\_) = 12 + \_\_\_ \) Now take the middle coefficient, \(\dfrac{5}{2} \). Divide it by 2. Dividing by 2 is the same as multiplying by \(\dfrac{1}{2} \). \(\dfrac{5}{2} \times \dfrac{1}{2} = \dfrac{5}{4} \) Now square it: \(\dfrac{25}{16} \) Now you add 25/16 to the left side inside the parentheses. \(2(x^2− \dfrac{5}{2}x + \dfrac{25}{16}) = 12 + \_\_\_ \) Once again, we have a factor of 2 outside the parentheses, so \(2 \times \dfrac{25}{16} = \dfrac{25}{8} \) That means we are really adding 25/8 to the left side, so we need to add 25/8 to teh right side. \(2(x^2− \dfrac{5}{2}x + \dfrac{25}{16}) = 12 + \dfrac{25}{8} \) Now we distribute the 2 on the left side: \(2x^2− 5x + \dfrac{25}{8} = 12 + \dfrac{25}{8} \)

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