1) x² + 9x + 18 = 0D = 9² - 4118 = 81 - 72 = 9x1 = (-9 + √9) / (21) = (-9 + 3) / 2 = -3 / 2x2 = (-9 - √9) / (21) = (-9 - 3) / 2 = -6
2) 9x² - 24x + 16 = 0D = 24² - 4916 = 576 - 576 = 0x = -b / (2a) = 24 / 18 = 4/3
3) 7x² + 20x - 3 = 0D = 20² - 47(-3) = 400 + 84 = 484x1 = (-20 + √484) / (27) = (-20 + 22) / 14 = 1/7x2 = (-20 - √484) / (27) = (-20 - 22) / 14 = -3
4) -6x² + 8x - 10 = 0D = 8² - 4(-6)(-10) = 64 - 240 = -176The discriminant is negative, so there are no real solutions.
5) -11x² + x = 0x(1 - 11x) = 0x1 = 0x2 = 1/11
6) x² - 0.04 = 0x² = 0.04x = √0.04 = 0.2 or x = -0.2
1) x² + 9x + 18 = 0
D = 9² - 4118 = 81 - 72 = 9
x1 = (-9 + √9) / (21) = (-9 + 3) / 2 = -3 / 2
x2 = (-9 - √9) / (21) = (-9 - 3) / 2 = -6
2) 9x² - 24x + 16 = 0
D = 24² - 4916 = 576 - 576 = 0
x = -b / (2a) = 24 / 18 = 4/3
3) 7x² + 20x - 3 = 0
D = 20² - 47(-3) = 400 + 84 = 484
x1 = (-20 + √484) / (27) = (-20 + 22) / 14 = 1/7
x2 = (-20 - √484) / (27) = (-20 - 22) / 14 = -3
4) -6x² + 8x - 10 = 0
D = 8² - 4(-6)(-10) = 64 - 240 = -176
The discriminant is negative, so there are no real solutions.
5) -11x² + x = 0
x(1 - 11x) = 0
x1 = 0
x2 = 1/11
6) x² - 0.04 = 0
x² = 0.04
x = √0.04 = 0.2 or x = -0.2