Completing The Square Method to Solve the Quadratic Equation


When a quadratic equation has a leading coefficient of 1 or is a difference of squares, it can often be solved by factoring. Then, we search for solutions using the zero-factor property.
Many quadratic equations with a leading coefficient other than 1 may be solved by factoring using t

.

As we all know, utilizing the quadratic formula to solve a quadratic equation is a simple process. However, pupils get a little perplexed when it is said that the quadratic equation should be solved by completing the square. If you are among those looking for an equation solution calculator, quadratic equation solver, equation balancer calculator, or quadratic function calculator to solve quadratic equations using the completing square approach, don't worry; we will fully explain how to do so. If you are stuck, you can always get help from the factoring equations calculator found on the internet.

Solving The Quadratic Equation Using the Square Method in Full. The steps we take to complete this honest approach are as follows:

 

Step 1: Equation Transposition

If necessary, transpose the equation first.

A quadratic equation may also be written in standard form.

 

Step 2: Make sure that X's coefficient is equal to 1

To get the coefficient of x to equal 1, divide the exponent of the x by the whole equation.

 

Step 3: Create a perfect square

Boost the value. Add the value (½×coefficientofx)2 to make the equation a perfect square. Add one to each side.

 

Step 4: Simplify the Equation

Simplify the numbers on the right side of the equation and square the left side.

 

Step 5: The Square Root, please.

After solving the equation using fundamental operations like addition and subtraction, we may get the value of x or the necessary solution sets. Use the square roots of both sides to do this.

Let's use the following examples to understand better completing the honest approach for solving quadratic equations:

 

Example

Use the square-foot approach to solve the equation.

X2–2x=2

 

Solution

Since the equation is already in standard form and the exponents of x don't need to be set to 1, we may skip the first and second steps in this case. Let's now begin with additional steps:

Add (1/2×b)2= (12×−2)2= (−1)2=1 Considering both sides of the issue,

 

X2–2x+1= 2+1

(x−1)2= 3

Taking the square root of the equation's two sides now,

√(x−1)2=√3(x−1)2=3

x−1=±√3x−1=±3

x=1±√3x=1±3

Solution sets {1–√31–3, 1+√31+3} Answer.

 

Quadratic Equation Applications

Quadratic equations may be used in more fields than only arithmetic, algebra, and geometry. It utilizes physics, chemistry, commerce, sports, law, and management. The great thing is that everything we see in everyday life that resembles a parabola can be solved using the quadratic equation since its graph shape is like one.

 

Calculator for quadratic formulas

In the past, we only used calculators for addition, subtraction, multiplication, and division. Still, in the modern age, we can quickly conduct all other calculations using specialized calculators, such as the quadratic formula calculator.

 

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