Pearl Angelie Villanueva Mahusay

Student’s Name Professor’s Name Subject DD MM YYYY Algebra Tasks Please solve the following problems: 1. Solve for x This problem involves quadratic equation. Often, the simplest way to solve a quadratic equation in the form: ax2 + bx + c = 0, for the value of x is by factoring or quadratic formula (López, Robles, and Martínez-Planell 3). To factor quadratic equation is to set each factor equal to zero, and then solve for each factor. While factoring may not always be successful, the quadratic formula may always find the solution. The Quadratic Formula is stated as . To solve for x in , we substitute the values of a, b, and c to the quadratic formula. For the equation above, the value of a = 1, b = 1, and c = 12. Thus,. Applying the necessary solution, the answers are x = 3 and -4. 2. Solve for x This problem involves exponential equations. One of the methods for solving exponential equations using the statement below: If bx = by, then x = y. This statement does require that the base in both exponentials to be the same (López, et. al. 5). To solve for 22x – 4 = 64, we have to create equivalent expressions in the equation that all have equal bases. Thus, . Since the bases are now the same, then two expressions are only equal if the exponents are also equal. Thus, 2x – 4 = 6. To solve for x, we move all terms not containing x to the right side of the equation. Thus, 2x = 10. We divide each term by 2 and simplify. The answer is x = 5. 3. Solve for x This problem involves trigonometric equation. Trigonometric equations use both the reference angles and trigonometric identities, as well as algebraic knowledge, to solve such equations. Particularly, trigonometric-ratio values in the first quadrant, how the unit circle works, and the relationship between radians and degrees, will be seen throughout the procedure. To solve , we may use the identity: . Simplifying the equation, we get: or . We let cos (x) = u. Substituting to , we have 3u – 2u2 + 2 = 0. The values of u are u = 2 and -1/2. Substituting the values of u back to the equation: u = cos (x), we get cos (x) = 2 and -1/2. By applying the values of cos using the periodic cycle in radians, the value of cos (x) = -1/2 will result to and . For the value of cos (x) = 2, the value of x = none. Works Cited López, Jonathan, Robles, Izraim and Martínez-Planell, Rafael. “Student’s Understanding of Quadratic Equations.” International Journal of Mathematical Education, vol. 15, no. 1, 2015, pp. 2- 24.