To solve these quadratic equations, we can rearrange them into standard form (ax^2 + bx + c = 0) and then use the quadratic formula to find the solutions.
0.3x - x^2 = 0 Rearrange the equation: x^2 - 0.3x = 0 Apply the quadratic formula: x = (0.3 ± sqrt((-0.3)^2 - 410)) / 2*1 x = (0.3 ± sqrt(0.09)) / 2 x = (0.3 ± 0.3) / 2 x = 0.6 / 2 = 0.3 The solutions to this equation are x = 0.3.
12 - 17x - 5x^2 = 0 Rearrange the equation: 5x^2 + 17x - 12 = 0 Apply the quadratic formula: x = (-17 ± sqrt(17^2 - 45(-12))) / 2*5 x = (-17 ± sqrt(289 + 240)) / 10 x = (-17 ± sqrt(529)) / 10 x = (-17 ± 23) / 10 The solutions are x = (23 - 17) / 10 = 0.6 and x = (-23 - 17) / 10 = -4.
7x - 4x^2 = -15 Rearrange the equation: 4x^2 - 7x + 15 = 0 Apply the quadratic formula: x = (7 ± sqrt((-7)^2 - 4415)) / 2*4 x = (7 ± sqrt(49 - 240)) / 8 x = (7 ± sqrt(-191)) / 8 Since the square root of -191 is imaginary, the solutions are complex numbers and cannot be expressed in the form of real numbers.
To solve these quadratic equations, we can rearrange them into standard form (ax^2 + bx + c = 0) and then use the quadratic formula to find the solutions.
0.3x - x^2 = 0
Rearrange the equation:
x^2 - 0.3x = 0
Apply the quadratic formula:
x = (0.3 ± sqrt((-0.3)^2 - 410)) / 2*1
x = (0.3 ± sqrt(0.09)) / 2
x = (0.3 ± 0.3) / 2
x = 0.6 / 2 = 0.3
The solutions to this equation are x = 0.3.
12 - 17x - 5x^2 = 0
Rearrange the equation:
5x^2 + 17x - 12 = 0
Apply the quadratic formula:
x = (-17 ± sqrt(17^2 - 45(-12))) / 2*5
x = (-17 ± sqrt(289 + 240)) / 10
x = (-17 ± sqrt(529)) / 10
x = (-17 ± 23) / 10
The solutions are x = (23 - 17) / 10 = 0.6 and x = (-23 - 17) / 10 = -4.
7x - 4x^2 = -15
Rearrange the equation:
4x^2 - 7x + 15 = 0
Apply the quadratic formula:
x = (7 ± sqrt((-7)^2 - 4415)) / 2*4
x = (7 ± sqrt(49 - 240)) / 8
x = (7 ± sqrt(-191)) / 8
Since the square root of -191 is imaginary, the solutions are complex numbers and cannot be expressed in the form of real numbers.