Answer :
2(x - 5)² + 13 = 31
2(x - 5)(x - 5) + 13 = 21
2(x(x - 5) - 5(x - 5)) + 13 = 21
2(x(x) - x(5) - 5(x) + 5(5)) + 13 = 21
2(x² - 5x - 5x + 25) + 13 = 21
2(x² - 10x + 25) + 13 = 21
2(x²) - 2(10x) + 2(25) + 13 = 21
2x² - 20x + 50 + 13 = 21
2x² - 20x + 63 = 21
- 21 - 21
2x² - 20x + 42 = 0
2(x²) - 2(20x) + 2(21) = 0
2(x² - 20x + 21) = 0
2 2
x² - 20x + 21 = 0
x = -(-20) +/- √((-20)² - 4(1)(21))
2(1)
x = 20 +/- √(400 - 84)
2
x = 20 +/- √(316)
2
x = 20 +/- 2√(79)
2
x = 10 + √(79)
x = 10 + √(79) U x = 10 - √(79)
2(x - 5)(x - 5) + 13 = 21
2(x(x - 5) - 5(x - 5)) + 13 = 21
2(x(x) - x(5) - 5(x) + 5(5)) + 13 = 21
2(x² - 5x - 5x + 25) + 13 = 21
2(x² - 10x + 25) + 13 = 21
2(x²) - 2(10x) + 2(25) + 13 = 21
2x² - 20x + 50 + 13 = 21
2x² - 20x + 63 = 21
- 21 - 21
2x² - 20x + 42 = 0
2(x²) - 2(20x) + 2(21) = 0
2(x² - 20x + 21) = 0
2 2
x² - 20x + 21 = 0
x = -(-20) +/- √((-20)² - 4(1)(21))
2(1)
x = 20 +/- √(400 - 84)
2
x = 20 +/- √(316)
2
x = 20 +/- 2√(79)
2
x = 10 + √(79)
x = 10 + √(79) U x = 10 - √(79)
