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Simplifying 6.73x2 + 2.63x = 5.43 Reorder the terms: 2.63x + 6.73x2 = 5.43 Solving 2.63x + 6.73x2 = 5.43 Solving for variable 'x'. Reorder the terms: -5.43 + 2.63x + 6.73x2 = 5.43 + -5.43 Combine like terms: 5.43 + -5.43 = 0.00 -5.43 + 2.63x + 6.73x2 = 0.00 Begin completing the square. Divide all terms by 6.73 the coefficient of the squared term: Divide each side by '6.73'. -0.8068350669 + 0.3907875186x + x2 = 0 Move the constant term to the right: Add '0.8068350669' to each side of the equation. -0.8068350669 + 0.3907875186x + 0.8068350669 + x2 = 0 + 0.8068350669 Reorder the terms: -0.8068350669 + 0.8068350669 + 0.3907875186x + x2 = 0 + 0.8068350669 Combine like terms: -0.8068350669 + 0.8068350669 = 0.0000000000 0.0000000000 + 0.3907875186x + x2 = 0 + 0.8068350669 0.3907875186x + x2 = 0 + 0.8068350669 Combine like terms: 0 + 0.8068350669 = 0.8068350669 0.3907875186x + x2 = 0.8068350669 The x term is 0.3907875186x. Take half its coefficient (0.1953937593). Square it (0.03817872117) and add it to both sides. Add '0.03817872117' to each side of the equation. 0.3907875186x + 0.03817872117 + x2 = 0.8068350669 + 0.03817872117 Reorder the terms: 0.03817872117 + 0.3907875186x + x2 = 0.8068350669 + 0.03817872117 Combine like terms: 0.8068350669 + 0.03817872117 = 0.84501378807 0.03817872117 + 0.3907875186x + x2 = 0.84501378807 Factor a perfect square on the left side: (x + 0.1953937593)(x + 0.1953937593) = 0.84501378807 Calculate the square root of the right side: 0.919246315 Break this problem into two subproblems by setting (x + 0.1953937593) equal to 0.919246315 and -0.919246315.Subproblem 1
x + 0.1953937593 = 0.919246315 Simplifying x + 0.1953937593 = 0.919246315 Reorder the terms: 0.1953937593 + x = 0.919246315 Solving 0.1953937593 + x = 0.919246315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1953937593' to each side of the equation. 0.1953937593 + -0.1953937593 + x = 0.919246315 + -0.1953937593 Combine like terms: 0.1953937593 + -0.1953937593 = 0.0000000000 0.0000000000 + x = 0.919246315 + -0.1953937593 x = 0.919246315 + -0.1953937593 Combine like terms: 0.919246315 + -0.1953937593 = 0.7238525557 x = 0.7238525557 Simplifying x = 0.7238525557Subproblem 2
x + 0.1953937593 = -0.919246315 Simplifying x + 0.1953937593 = -0.919246315 Reorder the terms: 0.1953937593 + x = -0.919246315 Solving 0.1953937593 + x = -0.919246315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1953937593' to each side of the equation. 0.1953937593 + -0.1953937593 + x = -0.919246315 + -0.1953937593 Combine like terms: 0.1953937593 + -0.1953937593 = 0.0000000000 0.0000000000 + x = -0.919246315 + -0.1953937593 x = -0.919246315 + -0.1953937593 Combine like terms: -0.919246315 + -0.1953937593 = -1.1146400743 x = -1.1146400743 Simplifying x = -1.1146400743Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7238525557, -1.1146400743}
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