HiSET Completing the Square — practice questions

1. Completing the square adds the square of half the coefficient of x. 2. The coefficient of x here is 14, and half of 14 is 7. 3. Squaring 7 gives 49, so 49 is the number to add. 4. Adding 28 doubles instead of squaring, and the result would not factor as a perfect square. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.2 Solve Quadratic Equations by Completing the Square_

1. Completing the square adds the square of half the coefficient of x to both sides. 2. Half of 10 is 5, and 5 squared is 25. 3. Adding 25 to both sides gives x squared plus 10x plus 25 equal to 49. 4. The left side is now a perfect square, so it factors as the bracket (x plus 5) squared. 5. Take the square root of both sides, keeping both signs, so x plus 5 equals 7 or negative 7. 6. The first branch gives x equal to 2 and the second gives x equal to negative 12. 7. Checking, 2 squared plus 10 times 2 is 4 plus 20, which is 24. 8. Checking the other, negative 12 squared is 144 and 10 times negative 12 is negative 120, and 144 minus 120 is 24. 9. The pair 2 and 12 keeps the wrong sign on the second branch. 10. The pair 5 and negative 5 solves only the halved coefficient rather than the equation. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.2 Solve Quadratic Equations by Completing the Square_