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SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE
  fractions formula adding subtracting, fractions formula adding subtracting multiplying ,   simplify radical expressions calculator root ,   solving second order nonlinear differential equations  
 Thank you for visiting our site! You landed on this page because you entered a search term similar to this: solving quadratic equations by completing the square.We have an extensive database of resources on solving quadratic equations by completing the square. Below is one of them. If you need further help, please take a look at our software "Algebrator", a software program that can solve any algebra problem you enter! 
2x + 7x = 4  
2x + 7x – 4 = 0 To get the equation in standard form, subtract 4 from each side; one side must be 0 when solving by factoring
(2x – 1)(x + 4) = 0 Factor left side of equation
2x – 1 = 0 or x + 4 = 0 Set each factor equal to 0, using the Zero Factor Property

2x = 1 x = -4

x =

Solve each of the resulting two equations

The solution set is

Solving Quadratic Equations Using the Square Root Property

A quadratic equation of the form x = kcan be solved using the following property:

Square Root Property: The solution set of x= kis

Example. Solve: a) 4x = 20

b) z = -49

Solution. a)

4x = 20  
Divide both sides by 4 to isolate x
Simplify
x = ± Use the square root property to obtain two solutions

The solution set is

b)

 

z= -49  
z = Use the square root property
z = ± 7i Simplify the radical

The solution set is

Solving Quadratic Equations by Completing the Square

To solve a quadratic equation by completing the square, theequation must be written in the form (x + n) = k.The following steps are used to solve the equation

ax+ bx + c = 0 , a ¹0 , by completing the square:

1. If a ¹ 1, divide both sidesof the equation by a.

2. Rewrite the equation so that the constant term is isolatedon one side of the equation.

3. Take half the coefficient of x and square this result; addthis square to both sides of the

equation.

4. Factor the resulting trinomial as a perfect square; combinelike terms on the other

side.

5. Use the square root property to complete the solution.

Example. Solve by completing the square: 2x + 5x– 4 = 0.

Solution.

2x + 5x – 4 = 0  
Divide both sides by 2
Add 2 to both sides to isolate the constant

Take half the coefficient of x and square it:

Add to both sides of the equation
Factor the trinomial; add the constants
Use the square root property
Add - to both sides and simplify the radical

The solution set is

 

Solving Quadratic Equations Using the Quadratic Formula

The solutions of the quadratic equation ax+ bx+ c = 0 , a ¹ 0, are

The following steps are used to solve a quadratic equationusing the quadratic formula:

1. Write the equation in standard form, ax+ bx+ c = 0.

2. Determine the values of a, b, and c; a is the coefficientof x, b is the coefficient of x,

and c is the constant.

3. Substitute these values of a, b, and c into the quadraticformula.

4. Simplify.

Example. Solve using the quadratic formula: 3x = 2x– 4

Solution.

3x = 2x – 4  
3x - 2x + 4 = 0 Write the equation in standard form.
a = 3, b = -2, c = 4 Determine the values of a, b, and c
The quadratic formula

Substitute the values of a, b, and c into the

formula

Simplify