Expand the equation and move all the terms to the left of the equal sign.
⟹ 2x 2 – 5x + 2 = 0
⟹ 2x 2 – 4x – x + 2 = 0
⟹ 2x (x – 2) – 1(x – 2) = 0
⟹ (x – 2) (2x – 1) = 0
Equate each factor equal to zero and solve
⟹ x – 2 = 0 or 2x – 1 = 0
⟹ x = 2 or x = 1212
Therefore, the solutions are x = 2, 1/2.
Example 2
Solve 3x 2 – 8x – 3 = 0
Solution
3x 2 – 9x + x – 3 = 0
⟹ 3x (x – 3) + 1(x – 3) = 0
⟹ (x – 3) (3x + 1) = 0
⟹ x = 3 or x = -13
Example 3
Solve the following quadratic equation (2x – 3)2 = 25
Solution
Expand the equation (2x – 3)2 = 25 to get;
⟹ 4x 2 – 12x + 9 – 25 = 0
⟹ 4x 2 – 12x – 16 = 0
Divide each term by 4 to get;
⟹ x 2 – 3x – 4 = 0
⟹ (x – 4) (x + 1) = 0
⟹ x = 4 or x = -1
The are many methods of factorizing quadratic equations. In this article, our emphasis will be based on how to factor quadratic equations, in which the coefficient of x2 is either 1 or greater than
Therefore, we will use the trial and error method to get the right factors for the given quadratic equation.
Answers & Comments
Answer:
Example 1
Solve: 2(x 2 + 1) = 5x
Solution
Expand the equation and move all the terms to the left of the equal sign.
⟹ 2x 2 – 5x + 2 = 0
⟹ 2x 2 – 4x – x + 2 = 0
⟹ 2x (x – 2) – 1(x – 2) = 0
⟹ (x – 2) (2x – 1) = 0
Equate each factor equal to zero and solve
⟹ x – 2 = 0 or 2x – 1 = 0
⟹ x = 2 or x = 1212
Therefore, the solutions are x = 2, 1/2.
Example 2
Solve 3x 2 – 8x – 3 = 0
Solution
3x 2 – 9x + x – 3 = 0
⟹ 3x (x – 3) + 1(x – 3) = 0
⟹ (x – 3) (3x + 1) = 0
⟹ x = 3 or x = -13
Example 3
Solve the following quadratic equation (2x – 3)2 = 25
Solution
Expand the equation (2x – 3)2 = 25 to get;
⟹ 4x 2 – 12x + 9 – 25 = 0
⟹ 4x 2 – 12x – 16 = 0
Divide each term by 4 to get;
⟹ x 2 – 3x – 4 = 0
⟹ (x – 4) (x + 1) = 0
⟹ x = 4 or x = -1
The are many methods of factorizing quadratic equations. In this article, our emphasis will be based on how to factor quadratic equations, in which the coefficient of x2 is either 1 or greater than
Therefore, we will use the trial and error method to get the right factors for the given quadratic equation.