Question

how to simplify quadratic equations?

Answer 1

A general quadratic equation can be written in the form ax2+bx+c=0. This calculator solves quadratic equation using two methods.

Method 1: Use the Quadratic Formula

When a≠0 , there are two solutions to ax2+bx+c=0 and they are

x=−b±b2−4ac−−−−−−−√2a.

The formula can be used to solve any quadratic equation.

Example:

Solve equation 2x2+7x−15=0 using the quadratic formula.

Solution:

Here we have : a=2 b=7 c=−15

x1,2=−b±b2−4ac−−−−−−−√2ax1,2=−7±72−4⋅2⋅(−15)−−−−−−−−−−−−−√2⋅2x1,2=−7±49+120−−−−−−−√4x1,2=−7±169−−−√4x1,2=−7±134To calculate first solution we use "+" sign:To calculate second solution we use "-" sign:x1=−7+134x1=64x1=32x2=−7−134x2=−204x2=−5

Exercise:

Solve equation 3x2 + 2x - 5 = 0. ( Use above calculator to check your solution. )

 

Method 2: Completing the square

The best way to learn this method is by using an example.

Example:

Solve equation 2x2 + 7x - 15 = 0 by completing the square.

Solution:

2x2+7x−15=02x2+7x−15=0/:2x2+72x−152=0Step1: Divide all terms by the coefficient of x2.x2+72x=152Step 2: Keep all terms containing x on one side. Move the constant to the right.x2+72x+(74)2=152+(74)2Step 3: Take half of the x-term coefficient and square it. Add this value to both sides.x2+72x+(74)2=16916Step 4: Simplify right side.(x+74)2=16916Step 5: Write the perfect square on the left.x+74=±16916−−−−√x+74=±134Step 6: Take the square root on both sides of the equation.x1=−74+134=32x2=−74−134=−5Step 7: Solve for x.