Solving Quadratic Equations: X<Sup>2</Sup> + 11X + 4

Solve for x in the equation x2 +11x+121/4=125/4 from e-eduanswers.com

Introduction

In mathematics, a quadratic equation is an equation of the form ax² + bx + c = 0, where x is the unknown, and a, b, and c are constants. Solving a quadratic equation means finding the values of x that make the equation true. In this article, we will discuss how to solve the quadratic equation x² + 11x + 4.

Factoring Method

The first method to solve the quadratic equation x² + 11x + 4 is the factoring method. To use this method, we need to find two numbers whose product is equal to 4 and whose sum is equal to 11. These numbers are 4 and 1. Therefore, we can write the quadratic equation as (x + 4)(x + 1) = 0. By using the zero product property, we get x + 4 = 0 or x + 1 = 0. Solving for x gives us x = -4 or x = -1.

Completing the Square Method

The second method to solve the quadratic equation x² + 11x + 4 is the completing the square method. To use this method, we need to rewrite the quadratic equation in the form (x + p)² + q = 0, where p and q are constants. First, we need to divide both sides of the equation by the coefficient of x², which is 1. This gives us x² + 11x/1 + 4/1 = 0. Next, we need to add and subtract (11/2)², which is (121/4), inside the parentheses. This gives us (x + 11/2)² - (121/4) + 4 = 0. Simplifying the equation gives us (x + 11/2)² - 105/4 = 0. Adding (105/4) to both sides of the equation gives us (x + 11/2)² = 105/4. Taking the square root of both sides of the equation gives us x + 11/2 = ±√(105/4). Solving for x gives us x = -11/2 ± √105/2.

Quadratic Formula Method

The third method to solve the quadratic equation x² + 11x + 4 is the quadratic formula method. The quadratic formula is x = (-b ± √(b² - 4ac))/2a, where a, b, and c are the constants in the quadratic equation ax² + bx + c = 0. In our case, a = 1, b = 11, and c = 4. Substituting these values in the quadratic formula gives us x = (-11 ± √(11² - 4(1)(4)))/2(1), which simplifies to x = (-11 ± √117)/2.

Conclusion

In conclusion, we have discussed three methods to solve the quadratic equation x² + 11x + 4. The factoring method gives us x = -4 or x = -1. The completing the square method gives us x = -11/2 ± √105/2. The quadratic formula method gives us x = (-11 ± √117)/2. These methods can be used to solve any quadratic equation, and it is important to be familiar with them in order to solve more complex equations.