Question

Solve for r by completing the saquare. round to the nearest hundredth if necessary.

a. 2r²-8r-10=0

Answer 1

To solve the quadratic equation 2r²-8r-10=0, we complete the square by moving the constant to the other side, dividing by the coefficient of r², taking the square root of both sides, and solving for r, resulting in two solutions: r = 5.00 and r = -1.00.

Step-by-step explanation:

To solve the quadratic equation 2r²-8r-10=0 by completing the square, we first need to move the constant term to the other side of the equation and then divide each term by the coefficient of the r² term to set the coefficient to 1. Here are the steps to achieve this:

1. First, we move the constant term to the other side: 2r² - 8r = 10.
2. Next, we divide each term by 2 to make the coefficient of r² equal to 1: r² - 4r = 5.
3. Now, to complete the square, we take half of the coefficient of r (which is -4) and square it, then add it to both sides of the equation: r² - 4r + 4 = 5 + 4.
4. This gives us a perfect square trinomial on the left: (r - 2)² = 9.
5. Finally, we take the square root of both sides: r - 2 = ±√9.
6. So, r = 2 ± 3, which gives us two solutions: r = 5 and r = -1.

If we round to the nearest hundredth, the solutions remain the same because they are whole numbers: r = 5.00 and r = -1.00.