Quadratic equations are mathematical equations of the form ax^2 + bx + c = 0, where a, b, and c are numbers and x is a variable. Solving these equations is an important part of algebra, and there are several methods of doing so. In this article, we will look at two specific examples, 55. x^2 – 3x + 2 and 58. 2x^2 – 9x^2, and explore how to solve them.
Solving Quadratic Equations
Quadratic equations can be solved using one of two methods: factoring or the quadratic formula. Factoring involves breaking the equation down into two separate equations, which can then be solved for x. The quadratic formula is an equation that can be used to solve for x directly.
Exploring 55. x^2 – 3x + 2
The first equation we will explore is 55. x^2 – 3x + 2. To solve for x, we can use either the factoring or quadratic formula methods.
Using the factoring method, we first need to identify two numbers whose product is 2 and whose sum is -3. The two numbers are -2 and 1. We can then factor the equation into two separate equations: x – 2 = 0 and x + 1 = 0. We can then solve each equation for x: x – 2 = 0 yields x = 2, and x + 1 = 0 yields x = -1.
Using the quadratic formula, we substitute the values of a, b, and c into the equation and solve for x. In this case, a = 1, b = -3, and c = 2. The equation then becomes x = (-b ± √b^2 – 4ac) / 2a. This yields x = (-(-3) ± √(-3)^2 – 4(1)(2)) / 2(1), or x = (3 ± √9 – 8) / 2. This simplifies to x = (3 ± 1) / 2, which yields x = 2 or x = -1.
Exploring 58. 2x^2 – 9x^2
The second equation we will explore is 58. 2x^2 – 9x^2. Again, we can use either the factoring or quadratic formula methods to solve for x.
Using the factoring method, we first need to identify two numbers whose product is –