Solving Quadratic Equations

To solve this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values of a, b, and c, we get: x = (-(-5) ± √((-5)^2 - 4(1)(6))) / 2(1). Simplifying this, we get: x = (5 ± √(25 - 24)) / 2. Further simplifying, we get: x = (5 ± 1) / 2. Therefore, x = 2 or x = 3.

To solve this equation, we can use factoring. We can factor the left-hand side as follows: (2x - 1)(x + 4) = 0. Setting each factor equal to 0, we get: 2x - 1 = 0 and x + 4 = 0. Solving these equations, we get: x = 1/2 and x = -4. Therefore, the solutions to the quadratic equation are x = 1 and x = -2.

To solve this equation, we can use the quadratic formula. Plugging in the values of a, b, and c, we get: x = (-(-2) ± √((-2)^2 - 4(3)(-8))) / 2(3). Simplifying this, we get: x = (2 ± √(4 + 96)) / 6. Further simplifying, we get: x = (2 ± √100) / 6. Therefore, x = 2 or x = -4/3.

To solve this equation, we can use completing the square. We can rewrite the left-hand side as follows: x^2 - 6x + 9 = (x - 3)^2. Setting this equal to 0, we get: (x - 3)^2 = 0. Taking the square root of both sides, we get: x - 3 = 0. Solving for x, we get: x = 3. Therefore, the only solution to the quadratic equation is x = 3.

To solve this equation, we can use the quadratic formula. Plugging in the values of a, b, and c, we get: x = (-12 ± √(12^2 - 4(4)(9))) / 2(4). Simplifying this, we get: x = (-12 ± √(144 - 144)) / 8. Further simplifying, we get: x = (-12 ± 0) / 8. Therefore, x = -3/2 or x = -3/2.

To solve this equation, we can use factoring. We can factor the left-hand side as follows: (2x - 1)(x - 2) = 0. Setting each factor equal to 0, we get: 2x - 1 = 0 and x - 2 = 0. Solving these equations, we get: x = 1/2 and x = 2. Therefore, the solutions to the quadratic equation are x = 1 and x = 2.

To solve this equation, we can use the quadratic formula. Plugging in the values of a, b, and c, we get: x = (-7 ± √(7^2 - 4(3)(2))) / 2(3). Simplifying this, we get: x = (-7 ± √(49 - 24)) / 6. Further simplifying, we get: x = (-7 ± √25) / 6. Therefore, x = -1 or x = -2.

To solve this equation, we can use factoring. We can factor the left-hand side as follows: (5x + 3)(x - 1) = 0. Setting each factor equal to 0, we get: 5x + 3 = 0 and x - 1 = 0. Solving these equations, we get: x = -3/5 and x = 1. Therefore, the solutions to the quadratic equation are x = 1 and x = -3.

To solve this equation, we can use the quadratic formula. Plugging in the values of a, b, and c, we get: x = (-3 ± √(3^2 - 4(2)(-5))) / 2(2). Simplifying this, we get: x = (-3 ± √(9 + 40)) / 4. Further simplifying, we get: x = (-3 ± √49) / 4. Therefore, x = 1 or x = -5.

To solve this equation, we can use completing the square. We can rewrite the left-hand side as follows: 4x^2 - 12x + 9 = (2x - 3)^2. Setting this equal to 0, we get: (2x - 3)^2 = 0. Taking the square root of both sides, we get: 2x - 3 = 0. Solving for x, we get: x = 3/2. Therefore, the only solution to the quadratic equation is x = 3/2.

To solve this equation, we can use factoring. We can factor the left-hand side as follows: (3x + 1)(x - 2) = 0. Setting each factor equal to 0, we get: 3x + 1 = 0 and x - 2 = 0. Solving these equations, we get: x = -1/3 and x = 2. Therefore, the solutions to the quadratic equation are x = 1 and x = -2.

To solve this equation, we can use the quadratic formula. Plugging in the values of a, b, and c, we get: x = (-7 ± √(7^2 - 4(2)(3))) / 2(2). Simplifying this, we get: x = (-7 ± √(49 - 24)) / 4. Further simplifying, we get: x = (-7 ± √25) / 4. Therefore, x = -1 or x = -3.

To solve this equation, we can use factoring. We can factor the left-hand side as follows: (5x + 2)(x - 1) = 0. Setting each factor equal to 0, we get: 5x + 2 = 0 and x - 1 = 0. Solving these equations, we get: x = -2/5 and x = 1. Therefore, the solutions to the quadratic equation are x = 1 and x = -2.

To solve this equation, we can use the quadratic formula. Plugging in the values of a, b, and c, we get: x = (-(-5) ± √((-5)^2 - 4(2)(2))) / 2(2). Simplifying this, we get: x = (5 ± √(25 - 16)) / 4. Further simplifying, we get: x = (5 ± √9) / 4. Therefore, x = 1 or x = 2.

To solve this equation, we can use the quadratic formula. Plugging in the values of a, b, and c, we get: x = (-7 ± √(7^2 - 4(3)(2))) / 2(3). Simplifying this, we get: x = (-7 ± √(49 - 24)) / 6. Further simplifying, we get: x = (-7 ± √25) / 6. Therefore, x = -1 or x = -2.