The Quadratic Formula is a useful tool for solving equations of the form ax2 + bx + c = 0. It can be used to solve a wide variety of equations, from ones with only one variable to those with multiple variables. In this article, we’ll be looking at how to use the Quadratic Formula to solve the equation x2 + 20 = 2x.
Understanding The Quadratic Formula
The Quadratic Formula is based on the idea that any equation of the form ax2 + bx + c = 0 can be solved by finding the values of x that make the equation true. To do this, we need to use the formula: x = [-b ± √(b2 – 4ac)] / 2a. This formula can be used to solve any equation that is in the form ax2 + bx + c = 0, where a, b, and c are all constants.
Solving X2 + 20 = 2x
To solve the equation x2 + 20 = 2x, we need to use the Quadratic Formula. We can plug the numbers into the formula to get: x = [-2 ± √(22 – 4(1)(20)] / 2(1). This simplifies to x = [-2 ± √(-60)] / 2. Since the square root of a negative number is not a real number, there are no real solutions to the equation. Therefore, the values of x are not real numbers.
In conclusion, the Quadratic Formula can be used to solve any equation of the form ax2 + bx + c = 0. In this article, we looked at how to use the formula to solve the equation x2 + 20 = 2x. Unfortunately, the values of x are not real numbers, as the square root of a negative number is not a real number.
The quadratic formula is a powerful tool used to solve equations with the general form of ax^2 + bx + c = 0. By substituting a, b, and c into the formula, one can calculate the values of x for which the equation is true.
Let’s use this formula to solve x^2 + 20 = 2x. First, we must identify the coefficients a, b, and c of the equation: a = 1, b = 2, and c = -20. The quadratic formula provides the following solution to the equation:
X = (-b ± √(b^2 – 4ac))/(2a)
Applying this formula to our equation yields two solutions:
X = (2 ± √48)/2 = (2 ± 4 √3)/2
Therefore, the values of x for which x^2 + 20 = 2x are x = 10 + 2√3 and x = 10 – 2√3.
This article outlines the steps necessary to use the quadratic formula to solve an equation with the form of x^2 + bx + c = 0. A worked example of using the formula to solve the equation x^2 + 20 = 2x was provided, and the solutions to the equation were identified as x = 10 + 2√3 and x = 10 – 2√3.