Solve the following quadratic equations by factoring.show the solution and checking 1. 2x² + 6x = 02. x² + 8x + 16 = 03. x² + 6x = 164. x² - 14 = 5x5. 3x² + 14x - 5 = 0
Answer (1)
Answer:1. 2x² + 6x = 02x(x + 3) = 02x = 0 ; x + 3 = 0Divide both sides by 2 ; Subtract 3 from both sidesx = 0 ; x = -32. x² + 8x + 16 = 0(x+4)(x+4) = 0(x+4)² = 0Take the square root of both sides.x+4 = 0 Subtract 4 from both sides.x = -43. x² + 6x = 16Subtract 16 from both sides.x² + 6x - 16 = 0(x + 8)(x - 2) = 0x + 8 = 0 ; x - 2 = 0Subtract 8 ; Add 2x = -8 ; x = 24. x² - 14 = 5xSubtract 5x from both sides.x² - 5x - 14 = 0(x - 7)(x + 2) = 0x - 7 = 0 ; x + 2 = 0Add 7 ; Subtract 2x = 7 ; x = x = -25. 3x² + 14x - 5 = 03x² + 15x - 1x - 5 = 0(3x² + 15x) - (1x + 5) = 03x(x + 5) - 1(x + 5) = 0(3x - 1)(x + 5) = 03x - 1 = 0 ; x + 5 = 0Add 1 ; Subtract 53x = 1 ; x = -5Divide both sides by 3x = 1/3 ; x = -5
