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Simplifying 11 + -6x = 0.8x2 Solving 11 + -6x = 0.8x2 Solving for variable 'x'. Combine like terms: 0.8x2 + -0.8x2 = 0.0 11 + -6x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -13.75 + 7.5x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 7.5x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 7.5x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 7.5x + x2 = 0 + 13.75 7.5x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 7.5x + x2 = 13.75 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 13.75 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 13.75 + 14.0625 Combine like terms: 13.75 + 14.0625 = 27.8125 14.0625 + 7.5x + x2 = 27.8125 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 27.8125 Calculate the square root of the right side: 5.273755777 Break this problem into two subproblems by setting (x + 3.75) equal to 5.273755777 and -5.273755777.Subproblem 1
x + 3.75 = 5.273755777 Simplifying x + 3.75 = 5.273755777 Reorder the terms: 3.75 + x = 5.273755777 Solving 3.75 + x = 5.273755777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 5.273755777 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 5.273755777 + -3.75 x = 5.273755777 + -3.75 Combine like terms: 5.273755777 + -3.75 = 1.523755777 x = 1.523755777 Simplifying x = 1.523755777Subproblem 2
x + 3.75 = -5.273755777 Simplifying x + 3.75 = -5.273755777 Reorder the terms: 3.75 + x = -5.273755777 Solving 3.75 + x = -5.273755777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -5.273755777 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -5.273755777 + -3.75 x = -5.273755777 + -3.75 Combine like terms: -5.273755777 + -3.75 = -9.023755777 x = -9.023755777 Simplifying x = -9.023755777Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.523755777, -9.023755777}
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