Expression Solutions
Expression Solutions
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complete each quadratic expression to make it a perfect square?
1. Complete each quadratic expression to make it a perfect:
A.
x ^ 2 - 16x + _____
B.
9r ^ 2 + 6r ______
2. Solve each equation by completing the square.
A.
c^2 + 6c - 9 = 0
B.
4m^2 - 12m - 7 = 0
C.
2x^2 - 8x + 5 = 0
3. Explain why b^2 - 6b + 12 = 0 has no solutions.
1a -- x² - 16x + 64 (64 is [16/2]² )
1b -- 9r² + 6r + 1 = (3r + 1)²
2a:
c² + 6c - 9 = 0
c² + 6c + 9 = 18
(c + 3)² = 18
c + 3 = ±√18
c = -3 ± 3√2
2b:
4m² - 12m = 7
4(m² - 3m + 9/4) = 7 + 4(9/4)
4(m - 3/2)² = 16
(m - 3/2)² = 4
m - 3/2 = ±2
m = 3/2 + 2 = 7/2 or
m = 3/2 - 2 = -1/2
2c:
2x² - 8x = -5
2(x² - 4x + 4) = -5 + 2(4)
(x - 2)² = 3
x = 2 ± √3
3:
b² - 6b + 12 = 0
(b² - 6b + 9) = -12 + 9
(b - 3)² = -3
b = 3 ± √-3
b = 3 ± i√3
equation has no REAL solutions because of √-n, but it has 2 complex number solutions.