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Simplifying 8.45x2 + 3.44x = 5.14 Reorder the terms: 3.44x + 8.45x2 = 5.14 Solving 3.44x + 8.45x2 = 5.14 Solving for variable 'x'. Reorder the terms: -5.14 + 3.44x + 8.45x2 = 5.14 + -5.14 Combine like terms: 5.14 + -5.14 = 0.00 -5.14 + 3.44x + 8.45x2 = 0.00 Begin completing the square. Divide all terms by 8.45 the coefficient of the squared term: Divide each side by '8.45'. -0.6082840237 + 0.4071005917x + x2 = 0 Move the constant term to the right: Add '0.6082840237' to each side of the equation. -0.6082840237 + 0.4071005917x + 0.6082840237 + x2 = 0 + 0.6082840237 Reorder the terms: -0.6082840237 + 0.6082840237 + 0.4071005917x + x2 = 0 + 0.6082840237 Combine like terms: -0.6082840237 + 0.6082840237 = 0.0000000000 0.0000000000 + 0.4071005917x + x2 = 0 + 0.6082840237 0.4071005917x + x2 = 0 + 0.6082840237 Combine like terms: 0 + 0.6082840237 = 0.6082840237 0.4071005917x + x2 = 0.6082840237 The x term is 0.4071005917x. Take half its coefficient (0.2035502959). Square it (0.04143272296) and add it to both sides. Add '0.04143272296' to each side of the equation. 0.4071005917x + 0.04143272296 + x2 = 0.6082840237 + 0.04143272296 Reorder the terms: 0.04143272296 + 0.4071005917x + x2 = 0.6082840237 + 0.04143272296 Combine like terms: 0.6082840237 + 0.04143272296 = 0.64971674666 0.04143272296 + 0.4071005917x + x2 = 0.64971674666 Factor a perfect square on the left side: (x + 0.2035502959)(x + 0.2035502959) = 0.64971674666 Calculate the square root of the right side: 0.806050089 Break this problem into two subproblems by setting (x + 0.2035502959) equal to 0.806050089 and -0.806050089.Subproblem 1
x + 0.2035502959 = 0.806050089 Simplifying x + 0.2035502959 = 0.806050089 Reorder the terms: 0.2035502959 + x = 0.806050089 Solving 0.2035502959 + x = 0.806050089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2035502959' to each side of the equation. 0.2035502959 + -0.2035502959 + x = 0.806050089 + -0.2035502959 Combine like terms: 0.2035502959 + -0.2035502959 = 0.0000000000 0.0000000000 + x = 0.806050089 + -0.2035502959 x = 0.806050089 + -0.2035502959 Combine like terms: 0.806050089 + -0.2035502959 = 0.6024997931 x = 0.6024997931 Simplifying x = 0.6024997931Subproblem 2
x + 0.2035502959 = -0.806050089 Simplifying x + 0.2035502959 = -0.806050089 Reorder the terms: 0.2035502959 + x = -0.806050089 Solving 0.2035502959 + x = -0.806050089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2035502959' to each side of the equation. 0.2035502959 + -0.2035502959 + x = -0.806050089 + -0.2035502959 Combine like terms: 0.2035502959 + -0.2035502959 = 0.0000000000 0.0000000000 + x = -0.806050089 + -0.2035502959 x = -0.806050089 + -0.2035502959 Combine like terms: -0.806050089 + -0.2035502959 = -1.0096003849 x = -1.0096003849 Simplifying x = -1.0096003849Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6024997931, -1.0096003849}
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