Lesson 17
Completing the Square and Complex Solutions
Problem 1
Find the solution or solutions to each equation.
- \(x^2+0.5x-14=0\)
- \(x^2+12x+36=0\)
- \(x^2-3x+8=0\)
- \(x^2+4=0\)
Solution
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Problem 2
Which describes the solutions to the equation \(x^2+7=0\)?
One real solution
Two real solutions
One non-real solution
Two non-real solutions
Solution
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Problem 3
Explain how you know \(\sqrt{3x+2}=\text-16\) has no solutions.
Solution
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(From Unit 3, Lesson 7.)Problem 4
Determine the number of real solutions and non-real solutions to each equation. Use the graphs; don't do any calculations to find the solutions.
- \(x^2-6x+7=0\)
- \(3x^2+2x+1=0\)
- \(\text-x^2-3x+2=0\)
- \(x^2-6x+7=\text-2\)
- \(\text-x^2-3x+2=6\)
- \(3x^2+2x+1=2\)
Solution
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Problem 5
- Write \((5-5i)^2\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers.
- Write \((5-5i)^4\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers.
Solution
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(From Unit 3, Lesson 14.)Problem 6
What number \(n\) makes this equation true?
\(x^2+11x+\frac{121}{4} = (x+n)^2\)
\(\frac{11}{4}\)
\(\frac{11}{2}\)
11
\(\frac{121}{4}\)
Solution
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(From Unit 3, Lesson 16.)