There are three ways to solve a quadratic equation.
ii) Quadratic formula
Here we are going to see, how to solve quadratic equation using completing the square method.
If the quadratic equation is in the form of ax^{2} + bx + c = 0
Step 1 :
Move the constant to the other side of the equal sign.
Step 2 :
Check if the leading coefficient of x^{2} is 1. If it is not 1, then divide the quadratic equation by the leading coefficient.
Step 3 :
Write the coefficient of x as multiple of 2.
Step 4 :
So far, the equation will be in the form of a^{2} + 2ab (or) a^{2} - 2ab
Step 5 :
Add b^{2} on both sides, and complete the formula for (a+b)^{2} or (a-b)^{2}
Step 6 :
Using square root property, solve for the variable x.
Solve for exact values of x by completing the square :
Problem 1 :
2x^{2 }+ 4x + 1 = 0
Solution :
2x^{2}+ 4x + 1 = 0
Divide each side by 2.
Add 1^{2} on each sides.
Take square root on both sides.
Problem 2 :
2x^{2} - 10x + 3 = 0
Solution :
2x^{2} - 10x + 3 = 0
Divide each side by 2.
Add (5/2)^{2} on each sides.
Take square root on both sides.
Problem 3 :
3x^{2} + 12x + 5 = 0
Solution :
3x^{2} + 12x + 5 = 0
Divide each side by 3.
Add 2^{2} on each sides.
Take square root on both sides.
Problem 4 :
3x^{2} = 6x + 4
Solution :
3x^{2} = 6x + 4
3x^{2} - 6x = 4
Divide each side by 3.
Add 1^{2} on each sides.
Take square root on both sides.
Problem 5 :
5x^{2} - 15x + 2 = 0
Solution :
5x^{2} - 15x + 2 = 0
Divide each side by 5.
Add (3/2)^{2} on each sides.
Take square root on both sides.
Problem 6 :
4x^{2} + 4x = 5
Solution :
4x^{2} + 4x = 5
Divide each side by 4.
Add 1^{2} on each sides.
Take square root on both sides.
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