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Simplifying 4 * 1.73x * x + 5x = 2 * 1.73 Multiply 4 * 1.73 6.92x * x + 5x = 2 * 1.73 Multiply x * x 6.92x2 + 5x = 2 * 1.73 Reorder the terms: 5x + 6.92x2 = 2 * 1.73 Multiply 2 * 1.73 5x + 6.92x2 = 3.46 Solving 5x + 6.92x2 = 3.46 Solving for variable 'x'. Reorder the terms: -3.46 + 5x + 6.92x2 = 3.46 + -3.46 Combine like terms: 3.46 + -3.46 = 0.00 -3.46 + 5x + 6.92x2 = 0.00 Begin completing the square. Divide all terms by 6.92 the coefficient of the squared term: Divide each side by '6.92'. -0.5 + 0.7225433526x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.7225433526x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.7225433526x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.7225433526x + x2 = 0 + 0.5 0.7225433526x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.7225433526x + x2 = 0.5 The x term is 0.7225433526x. Take half its coefficient (0.3612716763). Square it (0.1305172241) and add it to both sides. Add '0.1305172241' to each side of the equation. 0.7225433526x + 0.1305172241 + x2 = 0.5 + 0.1305172241 Reorder the terms: 0.1305172241 + 0.7225433526x + x2 = 0.5 + 0.1305172241 Combine like terms: 0.5 + 0.1305172241 = 0.6305172241 0.1305172241 + 0.7225433526x + x2 = 0.6305172241 Factor a perfect square on the left side: (x + 0.3612716763)(x + 0.3612716763) = 0.6305172241 Calculate the square root of the right side: 0.794051147 Break this problem into two subproblems by setting (x + 0.3612716763) equal to 0.794051147 and -0.794051147.Subproblem 1
x + 0.3612716763 = 0.794051147 Simplifying x + 0.3612716763 = 0.794051147 Reorder the terms: 0.3612716763 + x = 0.794051147 Solving 0.3612716763 + x = 0.794051147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3612716763' to each side of the equation. 0.3612716763 + -0.3612716763 + x = 0.794051147 + -0.3612716763 Combine like terms: 0.3612716763 + -0.3612716763 = 0.0000000000 0.0000000000 + x = 0.794051147 + -0.3612716763 x = 0.794051147 + -0.3612716763 Combine like terms: 0.794051147 + -0.3612716763 = 0.4327794707 x = 0.4327794707 Simplifying x = 0.4327794707Subproblem 2
x + 0.3612716763 = -0.794051147 Simplifying x + 0.3612716763 = -0.794051147 Reorder the terms: 0.3612716763 + x = -0.794051147 Solving 0.3612716763 + x = -0.794051147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3612716763' to each side of the equation. 0.3612716763 + -0.3612716763 + x = -0.794051147 + -0.3612716763 Combine like terms: 0.3612716763 + -0.3612716763 = 0.0000000000 0.0000000000 + x = -0.794051147 + -0.3612716763 x = -0.794051147 + -0.3612716763 Combine like terms: -0.794051147 + -0.3612716763 = -1.1553228233 x = -1.1553228233 Simplifying x = -1.1553228233Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4327794707, -1.1553228233}
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