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Simplifying (0.5x2) + 3x + -800 = 0 Reorder the terms: -800 + 3x + (0.5x2) = 0 Solving -800 + 3x + (0.5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -1600 + 6x + x2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 6x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 6x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 6x + x2 = 0 + 1600 6x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 6x + x2 = 1600 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 1600 + 9 Reorder the terms: 9 + 6x + x2 = 1600 + 9 Combine like terms: 1600 + 9 = 1609 9 + 6x + x2 = 1609 Factor a perfect square on the left side: ((x) + 3)((x) + 3) = 1609 Calculate the square root of the right side: 40.11234224 Break this problem into two subproblems by setting ((x) + 3) equal to 40.11234224 and -40.11234224.Subproblem 1
(x) + 3 = 40.11234224 Simplifying (x) + 3 = 40.11234224 x + 3 = 40.11234224 Reorder the terms: 3 + x = 40.11234224 Solving 3 + x = 40.11234224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 40.11234224 + -3 Combine like terms: 3 + -3 = 0 0 + x = 40.11234224 + -3 x = 40.11234224 + -3 Combine like terms: 40.11234224 + -3 = 37.11234224 x = 37.11234224 Simplifying x = 37.11234224Subproblem 2
(x) + 3 = -40.11234224 Simplifying (x) + 3 = -40.11234224 x + 3 = -40.11234224 Reorder the terms: 3 + x = -40.11234224 Solving 3 + x = -40.11234224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -40.11234224 + -3 Combine like terms: 3 + -3 = 0 0 + x = -40.11234224 + -3 x = -40.11234224 + -3 Combine like terms: -40.11234224 + -3 = -43.11234224 x = -43.11234224 Simplifying x = -43.11234224Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.11234224, -43.11234224}
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