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Simplifying 5.391668825x2 + -5.706062708x + 0.068393883 = 0 Reorder the terms: 0.068393883 + -5.706062708x + 5.391668825x2 = 0 Solving 0.068393883 + -5.706062708x + 5.391668825x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.391668825 the coefficient of the squared term: Divide each side by '5.391668825'. 0.0126851046 + -1.058311052x + x2 = 0 Move the constant term to the right: Add '-0.0126851046' to each side of the equation. 0.0126851046 + -1.058311052x + -0.0126851046 + x2 = 0 + -0.0126851046 Reorder the terms: 0.0126851046 + -0.0126851046 + -1.058311052x + x2 = 0 + -0.0126851046 Combine like terms: 0.0126851046 + -0.0126851046 = 0.0000000000 0.0000000000 + -1.058311052x + x2 = 0 + -0.0126851046 -1.058311052x + x2 = 0 + -0.0126851046 Combine like terms: 0 + -0.0126851046 = -0.0126851046 -1.058311052x + x2 = -0.0126851046 The x term is -1.058311052x. Take half its coefficient (-0.529155526). Square it (0.2800055707) and add it to both sides. Add '0.2800055707' to each side of the equation. -1.058311052x + 0.2800055707 + x2 = -0.0126851046 + 0.2800055707 Reorder the terms: 0.2800055707 + -1.058311052x + x2 = -0.0126851046 + 0.2800055707 Combine like terms: -0.0126851046 + 0.2800055707 = 0.2673204661 0.2800055707 + -1.058311052x + x2 = 0.2673204661 Factor a perfect square on the left side: (x + -0.529155526)(x + -0.529155526) = 0.2673204661 Calculate the square root of the right side: 0.517030431 Break this problem into two subproblems by setting (x + -0.529155526) equal to 0.517030431 and -0.517030431.Subproblem 1
x + -0.529155526 = 0.517030431 Simplifying x + -0.529155526 = 0.517030431 Reorder the terms: -0.529155526 + x = 0.517030431 Solving -0.529155526 + x = 0.517030431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.529155526' to each side of the equation. -0.529155526 + 0.529155526 + x = 0.517030431 + 0.529155526 Combine like terms: -0.529155526 + 0.529155526 = 0.000000000 0.000000000 + x = 0.517030431 + 0.529155526 x = 0.517030431 + 0.529155526 Combine like terms: 0.517030431 + 0.529155526 = 1.046185957 x = 1.046185957 Simplifying x = 1.046185957Subproblem 2
x + -0.529155526 = -0.517030431 Simplifying x + -0.529155526 = -0.517030431 Reorder the terms: -0.529155526 + x = -0.517030431 Solving -0.529155526 + x = -0.517030431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.529155526' to each side of the equation. -0.529155526 + 0.529155526 + x = -0.517030431 + 0.529155526 Combine like terms: -0.529155526 + 0.529155526 = 0.000000000 0.000000000 + x = -0.517030431 + 0.529155526 x = -0.517030431 + 0.529155526 Combine like terms: -0.517030431 + 0.529155526 = 0.012125095 x = 0.012125095 Simplifying x = 0.012125095Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.046185957, 0.012125095}
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