solve the algebra equation.

Question Description

I’m trying to learn for my Algebra class and I’m stuck. Can you help?

solve the equation by completing the square.

x^2 + 2x = 5

Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

Final Answer

x^2 + 2x = 5

First, before we can complete the square, we need to make sure that the x^2 and x terms are on the same side in order respectively, and the constant number (the number with no variable next to it) is on the other side of the equal sign.

x^2 + 2x = 5        <On the left side the x^2 term comes first and then the x term.  And the constant number is

                              on the right side.  Everything is ready for completing the square>

Next, we will let the variable 'b' represent the coefficient of x-term (regular x, not x^2).

x^2 + 2x = 5

The x-term is 2x,  and its coefficient is 2.   Therefore  b = 2

Third, find the value of (b/2)^2

            (b/2)^2    =    (2/2)^2                <Since b = 2, we substitute b with 2>

                                  1^2                     <Evaluate inside the parenthesis first>


Now, we are ready to complete the square to solve the equation.  The process is done as follows:

         x^2 + 2x = 5                   <Given equation>

         x^2 + 2x + 1  =  5 + 1     <Add both sides by your value of (b/2)^2 >

         x^2 + 2x + 1  =  6            <Evaluate the right side>

        (x+1)(x+1) = 6                  <The left side should represent a perfect square, so we can factor this side>

        (x+1)^2 = 6                       <x-expression must be in the form  (a + b)^2>

        sqrt[(x+1)^2] = sqrt(6)       <Take the square root of both sides>

        |x+1|  =  sqrt(6)                <Taking the square root of a squared expression cancels the exponent and the

                                                   inside expression is put in an absolute value expression>

       Keep in mind that if you have an absolute value expression set equal to a positive, we can solve for two cases.  A positive case, and a negative case.

                                          |x+1| = sqrt(6)

                       x + 1 = sqrt(6)       or       x + 1 = -sqrt(6)              <Two cases to solve for>

                  x + 1 - 1 = sqrt(6)  - 1     or      x + 1 - 1 =  -sqrt(6) - 1   <In both cases subtract both sides by 1>

                          x = sqrt(6) - 1        or      x = -sqrt(6) - 1

                          x = -1 + sqrt(6)      or     x = -1 - sqrt(6)

SOLUTION:    x = -1 + sqrt(6)     or    x = -1 - sqrt(6)


Wallace H (1013)
Rice University

Solid work, thanks.

The tutor was great. I’m satisfied with the service.

Goes above and beyond expectations !


Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors