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Simplifying 2.9x2 + -3.262x + 0.06525 = 0 Reorder the terms: 0.06525 + -3.262x + 2.9x2 = 0 Solving 0.06525 + -3.262x + 2.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.9 the coefficient of the squared term: Divide each side by '2.9'. 0.0225 + -1.124827586x + x2 = 0 Move the constant term to the right: Add '-0.0225' to each side of the equation. 0.0225 + -1.124827586x + -0.0225 + x2 = 0 + -0.0225 Reorder the terms: 0.0225 + -0.0225 + -1.124827586x + x2 = 0 + -0.0225 Combine like terms: 0.0225 + -0.0225 = 0.0000 0.0000 + -1.124827586x + x2 = 0 + -0.0225 -1.124827586x + x2 = 0 + -0.0225 Combine like terms: 0 + -0.0225 = -0.0225 -1.124827586x + x2 = -0.0225 The x term is -1.124827586x. Take half its coefficient (-0.562413793). Square it (0.3163092746) and add it to both sides. Add '0.3163092746' to each side of the equation. -1.124827586x + 0.3163092746 + x2 = -0.0225 + 0.3163092746 Reorder the terms: 0.3163092746 + -1.124827586x + x2 = -0.0225 + 0.3163092746 Combine like terms: -0.0225 + 0.3163092746 = 0.2938092746 0.3163092746 + -1.124827586x + x2 = 0.2938092746 Factor a perfect square on the left side: (x + -0.562413793)(x + -0.562413793) = 0.2938092746 Calculate the square root of the right side: 0.542041765 Break this problem into two subproblems by setting (x + -0.562413793) equal to 0.542041765 and -0.542041765.Subproblem 1
x + -0.562413793 = 0.542041765 Simplifying x + -0.562413793 = 0.542041765 Reorder the terms: -0.562413793 + x = 0.542041765 Solving -0.562413793 + x = 0.542041765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.562413793' to each side of the equation. -0.562413793 + 0.562413793 + x = 0.542041765 + 0.562413793 Combine like terms: -0.562413793 + 0.562413793 = 0.000000000 0.000000000 + x = 0.542041765 + 0.562413793 x = 0.542041765 + 0.562413793 Combine like terms: 0.542041765 + 0.562413793 = 1.104455558 x = 1.104455558 Simplifying x = 1.104455558Subproblem 2
x + -0.562413793 = -0.542041765 Simplifying x + -0.562413793 = -0.542041765 Reorder the terms: -0.562413793 + x = -0.542041765 Solving -0.562413793 + x = -0.542041765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.562413793' to each side of the equation. -0.562413793 + 0.562413793 + x = -0.542041765 + 0.562413793 Combine like terms: -0.562413793 + 0.562413793 = 0.000000000 0.000000000 + x = -0.542041765 + 0.562413793 x = -0.542041765 + 0.562413793 Combine like terms: -0.542041765 + 0.562413793 = 0.020372028 x = 0.020372028 Simplifying x = 0.020372028Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.104455558, 0.020372028}
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