Explanation Given Information: The provided quadratic equation is − 1 2 x 2 − 1 2 x + 1 = 0 . Formula used: The value of x in the equation a x 2 + b x + c = 0 can be given by the quadratic formula, x = − b ± b 2 − 4 a c 2 a where a , b and c are real numbers with a ≠ 0 . Calculation: Consider the quadratic equation − 1 2 x 2 − 1 2 x + 1 = 0 . Compare the above equation with the equation a x 2 + b x + c = 0 , a = − 1 2 , b = − 1 2 and c = 1 Put the values of a , b , c in the quadratic formula x = − b ± b 2 − 4 a c 2 a then simplify. x = − ( − 1 2 ) ± ( − 1 2 ) 2 − 4 ( − 1 2 ) ⋅ 1 2 ( − 1 2 ) = 1 2 ± 1 4 + 2 − 1 = 1 2 ± 9 4 − 1 = 1 2 ± 3 2 − 1 Further simplify, x = 1 2 ± 3 2 − 1 Therefore, = 1 2 + 3 2 − 1 = 1 + 3 2 − 1 = 4 2 − 1 = − 2 Or x = 1 2 − 3 2 − 1 = 1 − 3 2 − 1 = − 2 2 − 1 = 1 Check: For x = 1 Substitute the value of x = 1 in − 1 2 x 2 − 1 2 x + 1 = 0

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 0.5, Problem 22E

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To calculate: The all real solutions in the quadratic equation −12x2−12x+1=0.

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Chapter 0.5, Problem 21E

Chapter 0.5, Problem 23E

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For Exercises 31–56, perform the indicated operations. Write the answers in standard form, a + bi. (See Examples 3-6) 31. (2 – 7i) + (8 – 3i) 32. (6 – 10i) + (8 + 4i) 33. (15 + 21i) – (18 – 40i) 34. (250 + 100i) – (80 + 25i) 35. (2.3 + 4i) – (8.1 – 2.7i) + (4.6 – 6.7i) 36. (0.05 – 0.03i) + (-0.12 + 0.08i) – (0.07 + 0.05i) 37. 2i(5 + i) 38. 4i(6 + 5i) 39. (3 – 6i)(10 + i) 40. (2 – 5i)(8 + 2i) 43. (3 – V-5)(4 + V-5) 46. (3 – 21)? + (3 + 2i)? 41. (3 - 42. (10 — З1)? 44. (2 + V=7)(10 + V-7) 45. (2 – i)? + (2 + i)? 47. (10 – 4i)(10 + 4i) 48. (3 9i)(3 + 9i) 49. (V2 + V3i)(V2 - V3i) 50. (V3 + V7i)(V5 – Vīi) 6 + 2i 51. 3 - i 5 + i 52. 4 - i 8 - 5i 53. 13 + 2i 10 – 3i 54. 11 + 4i 55. 13i 56. 7i

In Exercises 23–25, solve each equation. If the solution set is Ø or (-0, ), classify the equation as an inconsistent equation or an identity. 23. 3(2x – 4) = 9 – 3(x + 1) 2x 24. x - 4 x + 1 4 2 4 25. 3(x – 4) + x = 2(6 + 2x)

Write each equation in STANDARD FROM

Chapter 0 Solutions

Applied Calculus

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Ch. 0.1 - Prob. 11E Ch. 0.1 - Prob. 12E Ch. 0.1 - Prob. 13E Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 15E Ch. 0.1 - Prob. 16E Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 18E Ch. 0.1 - Prob. 19E Ch. 0.1 - Prob. 20E Ch. 0.1 - Prob. 21E Ch. 0.1 - Prob. 22E Ch. 0.1 - Prob. 23E Ch. 0.1 - Prob. 24E Ch. 0.1 - Prob. 25E Ch. 0.1 - Prob. 26E Ch. 0.1 - Prob. 27E Ch. 0.1 - Prob. 28E Ch. 0.1 - Prob. 29E Ch. 0.1 - Prob. 30E Ch. 0.1 - Prob. 31E Ch. 0.1 - Prob. 32E Ch. 0.1 - Prob. 33E Ch. 0.1 - Prob. 34E Ch. 0.1 - Prob. 35E Ch. 0.1 - Prob. 36E Ch. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Prob. 38E Ch. 0.1 - Prob. 39E Ch. 0.1 - Prob. 40E Ch. 0.1 - Prob. 41E Ch. 0.1 - Prob. 42E Ch. 0.1 - Prob. 43E Ch. 0.1 - Prob. 44E Ch. 0.1 - Prob. 45E Ch. 0.1 - Prob. 46E Ch. 0.1 - Prob. 47E Ch. 0.1 - Prob. 48E Ch. 0.1 - Prob. 49E Ch. 0.1 - Prob. 50E Ch. 0.2 - Evaluate the expression sin Exercises 116. 33 Ch. 0.2 - Prob. 2E Ch. 0.2 - Evaluate the expression sin Exercises 116. 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The all real solutions in the quadratic equation − 1 2 x 2 − 1 2 x + 1 = 0 .

Solution Summary: The author calculates the quadratic equation -12x2, which has two distinct real solutions.

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To calculate: The all real solutions in the quadratic equation −12x2−12x+1=0.

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Chapter 0 Solutions