Find the zeros of the quadratic equation \(2x^2 - 8x - 10 = 0\) by completing the square.
Answer
Step 5: Solve each equation for x to get the zeros of the original quadratic equation. This gives us \(x = 2 + 3\) or \(x = 2 - 3\).
Step 1 ：Step 1: Divide every term by 2 to simplify the equation. This gives us \(x^2 - 4x - 5 = 0\).
Step 2 ：Step 2: Rearrange the equation to isolate the square terms on one side: \(x^2 - 4x = 5\).
Step 3 ：Step 3: Complete the square on the left side of the equation by adding the square of half the coefficient of x to both sides of the equation. This gives us \((x - 2)^2 = 9\).
Step 4 ：Step 4: Take the square root of both sides to solve for x. This gives us two possible solutions: \(x - 2 = 3\) or \(x - 2 = -3\).
Step 5 ：Step 5: Solve each equation for x to get the zeros of the original quadratic equation. This gives us \(x = 2 + 3\) or \(x = 2 - 3\).
