logo for solving-math-problems.com
leftimage for solving-math-problems.com

Solve for x

by Mohammed
(South Africa)











































solve the following quadratic equation for x

x² + x² + 2x = 100


In general, you can use 5 different approaches:

(A) Factoring
(B) Quadratic Formula
(C) Completing the Square
(D) the Indian Method
(E) Graphical solution

Comments for Solve for x

Click here to add your own comments

Aug 18, 2011
Solve Quadratic Equation
by: Staff

------------------------------------------------

Part II


(1) Click the following link to VIEW the graphical solution; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/quad-eq-2011-08-18.png



check the solution by substituting the two numerical values of x into the original equation

for x ≈ -7.58872


x² + x² + 2x = 100

(-7.58872)² + (-7.58872)² + 2*(-7.58872) = 100

57.5887 + 57.5887 - 15.1774= 100

115.177 - 15.177 = 100

100 = 100, OK → x ≈ -7.58872 is a valid solution



for x ≈ 6.58872


x² + x² + 2x = 100

(6.58872)² + (6.58872)² + 2*(6.58872) = 100

43.4112 + 43.4112 + 13.1774 = 100


99.9998 ≈ 100, OK → x ≈ 6.58872 is a valid solution




Thanks for writing.

Staff
www.solving-math-problems.com



Aug 18, 2011
Solve Quadratic Equation
by: Staff


Part I

The question:

by Mohammed
(South Africa)

solve for x

x² + x² + 2x = 100


The answer:

x² + x² + 2x = 100


Combine like terms

(x² + x²) + 2x = 100

(2x²) + 2x = 100

2x² + 2x = 100


Divide each side of the equation by 2 to simplify the equation

(2x² + 2x)/2 = 100/2

(2/2)*x² + (2/2)*x = 100/2

(1)*x² + (1)*x = 100/2

x² + x = 100/2

x² + x = 50


At this point, you have 5 choices on how to proceed to the solution:

(1) Solve by Factoring [this will not work for this equation]
(2) Use the Quadratic Formula
(3) Complete the Square
(4) Use the Indian Method for solving a quadratic equation (similar to completing the square)
(5) Solve the equation graphically

I am going to solve this equation using the Indian Method because I think it will be easier for you to follow.

The steps used in the Indian Method are:

(a) Move the constant term to the right side of the equation.
(b) Multiply each term in the equation by four times the coefficient of the x squared term.
(c) Square the coefficient of the original x term and add it to both sides of the equation.
(d) Take the square root of both sides.
(e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x.
(f) Set the left side of equation equal to the negative square root of the number on the right side of the equation and solve for x.


Equation: x² + x = 50


(a) Move the constant term to the right side of the equation.

The constant is already on the right side of the equation

x² + x = 50


(b) Multiply each term in the equation by four times the coefficient of the x squared term.

The coefficient of the x² term is 1.

x² + x = 50

(4 * 1) * (x² + x = 50)

(4) * (x² + x = 50)

(4)*x² + (4)*(x) = (4)*(50)

4x² + 4x = 200



(c) Square the coefficient of the original x term and add it to both sides of the equation.

The coefficient of the original x term is 1.

(1)² = 1

4x² + 4x + 1 = 200 + 1

4x² + 4x + 1 = 201


(d) Take the square root of both sides.

4x² + 4x + 1 = 201

sqrt(4x² + 4x + 1) = sqrt(201)

sqrt(2x + 1)² = sqrt(201)

2x + 1 = sqrt(201)

2x + 1 = ±√(201)


(e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x.

2x + 1 = +√(201)

2x + 1 - 1 = +√(201) - 1

2x + 0 = +√(201) - 1

2x = +√(201) - 1

2x/2 = [+√(201) - 1]/2

(2/2)*x = [+√(201) - 1]/2

(1)*x = [+√(201) - 1]/2

x = [+√(201) - 1]/2

x ≈ (14.1774468787578 - 1) - 1]/2

x ≈ (13.1774468787578)/2

x ≈ 6.58872


(f) Set the left side of equation equal to the negative square root of the number on the right side of the equation and solve for x.

2x + 1 = -√(201)

2x + 1 - 1 = -√(201) - 1

2x + 0 = -√(201) - 1

2x = -√(201) - 1

2x/2 = [-√(201) - 1]/2

(2/2)*x = [-√(201) - 1]/2

(1)*x = [-√(201) - 1]/2

x = [-√(201) - 1]/2

x ≈ (-14.1774468787578 - 1) - 1]/2

x ≈ (-15.1774468787578)/2

x ≈ -7.58872


the final solution is: x ∈ {-7.58872, 6.58872}

------------------------------------------------

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com