Which Equation Shows The Quadratic Formula Used Correctly To Solve 5X2 + 3X – 4 = 0 For X?

The quadratic equation is one of the most important equations to know when studying mathematics. It can be used to solve for relationships between two variables and has many practical applications in areas such as physics, engineering, and finance. In this article, we will look at how the quadratic formula can be used correctly to solve the equation 5×2 + 3x – 4 = 0 for x. We will go through the steps needed and explain why each step is important in order to get the correct solution.

The Quadratic Formula

To solve a quadratic equation, we can use the Quadratic Formula. This formula tells us that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +/- sqrt(b^2 – 4ac)) / (2a)

For our equation, we have a = 1, b = 2, and c = -1. Plugging these values into the Quadratic Formula, we get:

x = (-2 +/- sqrt(4 – 4(-1))) / (2(1))

x = (-2 +/- sqrt(16)) / 2

x = [-2 +/- 4] / 2

So our solutions are x = 0 and x = -1.

How to solve 5X2 + 3X – 4 = 0 for X using the Quadratic Formula

To solve 5X2 + 3X – 4 = 0 for X using the Quadratic Formula, we need to first understand what the Quadratic Formula is and how it works. The Quadratic Formula is a mathematical formula used to solve quadratic equations ( equations that have a second-degree polynomial in them). The standard form of a quadratic equation is:

Ax^2 + Bx + C = 0

The Quadratic Formula can be used to solve for the value of x in this equation. The formula is as follows:

x = -b +/- sqrt(b^2 – 4ac) / 2a

In our equation, 5X2 + 3X – 4 = 0, we have A = 5, B = 3, and C = -4. Plugging these values into the Quadratic Formula, we get:

x = -3 +/- sqrt(9 – 20) / 10

x = -3 +/- sqrt(-11) / 10

The answer

There are a few different ways to solve this equation for x, but only one way is using the quadratic formula correctly. The quadratic formula is:

x = -b ± √(b^2-4ac)/2a

To solve this equation using the quadratic formula, we need to first identify a, b, and c. In this equation, a=1, b=2, and c=-3. Plugging these values into the quadratic formula gives us:

x = -2 ± √(4-4(-3))/2(1)

x = -2 ± √16/2

x = -2 ± 4/2

x = -2 ± 2

The two solutions for x are 0 and -4.

Why the Quadratic Formula is important

The Quadratic Formula is important because it provides a way to solve for x when given an equation that is in the form of ax^2 + bx + c = 0. This is important because it allows us to find the roots of a quadratic equation, which can be used to find the points of intersection of a parabola with a line. Additionally, the Quadratic Formula can be used to find the maximum or minimum value of a quadratic function, as well as the axis of symmetry.

Conclusion

In conclusion, the correct equation to use when solving 5X2 + 3X – 4 = 0 for X is X = (-3 ± √(3^2 – 4*5*(-4)))/(2*5). This equation uses the quadratic formula correctly and should help you find the two solutions to this equation. Knowing how to apply the quadratic formula correctly can come in handy when tackling more difficult equations with multiple variables, so it’s a good idea to practice using it on different types of problems.