Solve the following equations by using quadratic formula

Answer: 1.) 4x² - 31x + 42 = 0 a = 4, b = -31, c = 42x = (-b ± √(b² - 4ac)) / 2ax = (31 ± √((-31)² - 4 * 4 * 42)) / (2 * 4)x = (31 ± √(961 - 672)) / 8x = (31 ± √289) / 8x = (31 ± 17) / 8x1 = (31 + 17) / 8 = 6x2 = (31 - 17) / 8 = 7/4x = 6 or x = 7/4 2.) 9x² + 9x + 2 = 0 a=9, b= 9 c= 2x = (-b ± √(b² - 4ac)) / 2ax = (-9 ± √(9² - 4 * 9 * 2)) / (2 * 9)x = (-9 ± √(81 - 72)) / 18x = (-9 ± √9) / 18x = (-9 ± 3) / 18x1 = (-9 + 3) / 18 = -1/3x2 = (-9 - 3) / 18 = -2/3x = -1/3 or x = -2/3 3.) x² + 16x - 420 = 0 a = 1, b = 16, c = -420x = (-b ± √(b² - 4ac)) / 2ax = (-16 ± √(16² - 4 * 1 * -420)) / (2 * 1)x = (-16 ± √(256 + 1680)) / 2x = (-16 ± √1936) / 2x = (-16 ± 44) / 2x1 = (-16 + 44) / 2 = 14x2 = (-16 - 44) / 2 = -30- Solutions: x = 14 or x = -30 4.) 33x² + 39x + 31 = 0 a = 33, b = 39, c = 31x = (-b ± √(b² - 4ac)) / 2ax = (-39 ± √(39² - 4 * 33 * 31)) / (2 * 33)x = (-39 ± √(1521 - 4092)) / 66x = (-39 ± √(-2571)) / 66x = (-39 ± √2571 * i) / 66 (where 'i' is the imaginary unit, √-1)x1 = (-39 + √2571 * i) / 66x2 = (-39 - √2571 * i) / 66x = (-39 + √2571 * i) / 66 or x = (-39 - √2571 * i) / 66 5.) x² + 9x = -18 - Rewrite the equation in standard form: x² + 9x + 18 = 0 a = 1, b = 9, c = 18x = (-b ± √(b² - 4ac)) / 2ax = (-9 ± √(9² - 4 * 1 * 18)) / (2 * 1)x = (-9 ± √(81 - 72)) / 2x = (-9 ± √9) / 2x = (-9 ± 3) / 2x1 = (-9 + 3) / 2 = -3x2 = (-9 - 3) / 2 = -6x = -3 or x = -6

Answered by leatrinanes12 | 2024-09-03