Solve the quadratic equation (2x^2 - 6x - 8 = 0) by completing the square.

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Accepted Answer

Step:1 ：Firstly, divide the equation by the coefficient of (x^2), which is 2, to make it (x^2 - 3x - 4 = 0)Step:2 ：Next, rewrite the equation as (x^2 - 3x = 4)Step:3 ：Now, take half of the coefficient of (x), square it and add it to both sides of the equation. Half of -3 is -1.5 and (-1.5^2 = 2.25), so we add 2.25 to both sides to get ((x - 1.5)^2 = 6.25)Step:4 ：Finally, take the square root of both sides and solve for (x), which gives (x = 1.5 + sqrt{6.25}) and (x = 1.5 - sqrt{6.25})

Answer

Step: 1 ：Firstly, divide the equation by the coefficient of (x^2), which is 2, to make it (x^2 - 3x - 4 = 0)Step: 2 ：Next, rewrite the equation as (x^2 - 3x = 4)Step: 3 ：Now, take half of the coefficient of (x), square it and add it to both sides of the equation. Half of -3 is -1.5 and (-1.5^2 = 2.25), so we add 2.25 to both sides to get ((x - 1.5)^2 = 6.25)Step: 4 ：Finally, take the square root of both sides and solve for (x), which gives (x = 1.5 + sqrt{6.25}) and (x = 1.5 - sqrt{6.25})

Solve the quadratic equation \(2x^2 - 6x - 8 = 0\) by completing the square.

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