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Simplifying 0.56x2 + -3.2x + 708.28 = 704 Reorder the terms: 708.28 + -3.2x + 0.56x2 = 704 Solving 708.28 + -3.2x + 0.56x2 = 704 Solving for variable 'x'. Reorder the terms: 708.28 + -704 + -3.2x + 0.56x2 = 704 + -704 Combine like terms: 708.28 + -704 = 4.28 4.28 + -3.2x + 0.56x2 = 704 + -704 Combine like terms: 704 + -704 = 0 4.28 + -3.2x + 0.56x2 = 0 Begin completing the square. Divide all terms by 0.56 the coefficient of the squared term: Divide each side by '0.56'. 7.642857143 + -5.714285714x + x2 = 0 Move the constant term to the right: Add '-7.642857143' to each side of the equation. 7.642857143 + -5.714285714x + -7.642857143 + x2 = 0 + -7.642857143 Reorder the terms: 7.642857143 + -7.642857143 + -5.714285714x + x2 = 0 + -7.642857143 Combine like terms: 7.642857143 + -7.642857143 = 0.000000000 0.000000000 + -5.714285714x + x2 = 0 + -7.642857143 -5.714285714x + x2 = 0 + -7.642857143 Combine like terms: 0 + -7.642857143 = -7.642857143 -5.714285714x + x2 = -7.642857143 The x term is -5.714285714x. Take half its coefficient (-2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. -5.714285714x + 8.163265305 + x2 = -7.642857143 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714x + x2 = -7.642857143 + 8.163265305 Combine like terms: -7.642857143 + 8.163265305 = 0.520408162 8.163265305 + -5.714285714x + x2 = 0.520408162 Factor a perfect square on the left side: (x + -2.857142857)(x + -2.857142857) = 0.520408162 Calculate the square root of the right side: 0.721393209 Break this problem into two subproblems by setting (x + -2.857142857) equal to 0.721393209 and -0.721393209.Subproblem 1
x + -2.857142857 = 0.721393209 Simplifying x + -2.857142857 = 0.721393209 Reorder the terms: -2.857142857 + x = 0.721393209 Solving -2.857142857 + x = 0.721393209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + x = 0.721393209 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = 0.721393209 + 2.857142857 x = 0.721393209 + 2.857142857 Combine like terms: 0.721393209 + 2.857142857 = 3.578536066 x = 3.578536066 Simplifying x = 3.578536066Subproblem 2
x + -2.857142857 = -0.721393209 Simplifying x + -2.857142857 = -0.721393209 Reorder the terms: -2.857142857 + x = -0.721393209 Solving -2.857142857 + x = -0.721393209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + x = -0.721393209 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = -0.721393209 + 2.857142857 x = -0.721393209 + 2.857142857 Combine like terms: -0.721393209 + 2.857142857 = 2.135749648 x = 2.135749648 Simplifying x = 2.135749648Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.578536066, 2.135749648}
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