The solution of the given equation x + 8 = 2 + x . The solution of the given equation is x = 1 . Calculation: Consider the provided equation, x + 8 = 2 + x Square each side and solve, x + 8 = 2 + x 2 x + 8 = 4 + x 2 + 4 x Write the above equation in standard form. x 2 + 3 x − 4 = 0 Now factorize the above equation, x + 4 x − 1 = 0 Put the first factor equal to zero to get, x + 4 = 0 x = − 4 Then put the second factor equal to zero to get, x − 1 = 0 x = 1 Check: Put x = − 4 , 1 in the equation x + 8 = 2 + x . First, put x = − 4 . − 4 + 8 = ? 2 + − 4 4 = ? − 2 2 ≠ − 2 So, x = − 4 is an extraneous solution. Now put x = 1 1 + 8 = ? 2 + 1 9 = ? 3 3 = 3 It is true. Hence, the solution of the given equation is x = 1 .
The solution of the given equation x + 8 = 2 + x . The solution of the given equation is x = 1 . Calculation: Consider the provided equation, x + 8 = 2 + x Square each side and solve, x + 8 = 2 + x 2 x + 8 = 4 + x 2 + 4 x Write the above equation in standard form. x 2 + 3 x − 4 = 0 Now factorize the above equation, x + 4 x − 1 = 0 Put the first factor equal to zero to get, x + 4 = 0 x = − 4 Then put the second factor equal to zero to get, x − 1 = 0 x = 1 Check: Put x = − 4 , 1 in the equation x + 8 = 2 + x . First, put x = − 4 . − 4 + 8 = ? 2 + − 4 4 = ? − 2 2 ≠ − 2 So, x = − 4 is an extraneous solution. Now put x = 1 1 + 8 = ? 2 + 1 9 = ? 3 3 = 3 It is true. Hence, the solution of the given equation is x = 1 .
Solution Summary: The author calculates the solution of the given equation sqrtx+8=2+x.
Exercise #1: Consider the simple equation x =11.
(a) What values of x would solve this equation?
Explain.
(b) Use your answer to (a) to help solve the
equation x-5=11.
Chapter 1 Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.