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Simplifying 1.12 = 0.64 + 0.63x + 0.53x2 Solving 1.12 = 0.64 + 0.63x + 0.53x2 Solving for variable 'x'. Combine like terms: 1.12 + -0.64 = 0.48 0.48 + -0.63x + -0.53x2 = 0.64 + 0.63x + 0.53x2 + -0.64 + -0.63x + -0.53x2 Reorder the terms: 0.48 + -0.63x + -0.53x2 = 0.64 + -0.64 + 0.63x + -0.63x + 0.53x2 + -0.53x2 Combine like terms: 0.64 + -0.64 = 0.00 0.48 + -0.63x + -0.53x2 = 0.00 + 0.63x + -0.63x + 0.53x2 + -0.53x2 0.48 + -0.63x + -0.53x2 = 0.63x + -0.63x + 0.53x2 + -0.53x2 Combine like terms: 0.63x + -0.63x = 0.00 0.48 + -0.63x + -0.53x2 = 0.00 + 0.53x2 + -0.53x2 0.48 + -0.63x + -0.53x2 = 0.53x2 + -0.53x2 Combine like terms: 0.53x2 + -0.53x2 = 0.00 0.48 + -0.63x + -0.53x2 = 0.00 Begin completing the square. Divide all terms by -0.53 the coefficient of the squared term: Divide each side by '-0.53'. -0.9056603774 + 1.188679245x + x2 = 0 Move the constant term to the right: Add '0.9056603774' to each side of the equation. -0.9056603774 + 1.188679245x + 0.9056603774 + x2 = 0 + 0.9056603774 Reorder the terms: -0.9056603774 + 0.9056603774 + 1.188679245x + x2 = 0 + 0.9056603774 Combine like terms: -0.9056603774 + 0.9056603774 = 0.0000000000 0.0000000000 + 1.188679245x + x2 = 0 + 0.9056603774 1.188679245x + x2 = 0 + 0.9056603774 Combine like terms: 0 + 0.9056603774 = 0.9056603774 1.188679245x + x2 = 0.9056603774 The x term is 1.188679245x. Take half its coefficient (0.5943396225). Square it (0.3532395869) and add it to both sides. Add '0.3532395869' to each side of the equation. 1.188679245x + 0.3532395869 + x2 = 0.9056603774 + 0.3532395869 Reorder the terms: 0.3532395869 + 1.188679245x + x2 = 0.9056603774 + 0.3532395869 Combine like terms: 0.9056603774 + 0.3532395869 = 1.2588999643 0.3532395869 + 1.188679245x + x2 = 1.2588999643 Factor a perfect square on the left side: (x + 0.5943396225)(x + 0.5943396225) = 1.2588999643 Calculate the square root of the right side: 1.122007114 Break this problem into two subproblems by setting (x + 0.5943396225) equal to 1.122007114 and -1.122007114.Subproblem 1
x + 0.5943396225 = 1.122007114 Simplifying x + 0.5943396225 = 1.122007114 Reorder the terms: 0.5943396225 + x = 1.122007114 Solving 0.5943396225 + x = 1.122007114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5943396225' to each side of the equation. 0.5943396225 + -0.5943396225 + x = 1.122007114 + -0.5943396225 Combine like terms: 0.5943396225 + -0.5943396225 = 0.0000000000 0.0000000000 + x = 1.122007114 + -0.5943396225 x = 1.122007114 + -0.5943396225 Combine like terms: 1.122007114 + -0.5943396225 = 0.5276674915 x = 0.5276674915 Simplifying x = 0.5276674915Subproblem 2
x + 0.5943396225 = -1.122007114 Simplifying x + 0.5943396225 = -1.122007114 Reorder the terms: 0.5943396225 + x = -1.122007114 Solving 0.5943396225 + x = -1.122007114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5943396225' to each side of the equation. 0.5943396225 + -0.5943396225 + x = -1.122007114 + -0.5943396225 Combine like terms: 0.5943396225 + -0.5943396225 = 0.0000000000 0.0000000000 + x = -1.122007114 + -0.5943396225 x = -1.122007114 + -0.5943396225 Combine like terms: -1.122007114 + -0.5943396225 = -1.7163467365 x = -1.7163467365 Simplifying x = -1.7163467365Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5276674915, -1.7163467365}
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