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Simplifying 0.56x2 + -3.2x + 708.28 = 706 Reorder the terms: 708.28 + -3.2x + 0.56x2 = 706 Solving 708.28 + -3.2x + 0.56x2 = 706 Solving for variable 'x'. Reorder the terms: 708.28 + -706 + -3.2x + 0.56x2 = 706 + -706 Combine like terms: 708.28 + -706 = 2.28 2.28 + -3.2x + 0.56x2 = 706 + -706 Combine like terms: 706 + -706 = 0 2.28 + -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'. 4.071428571 + -5.714285714x + x2 = 0 Move the constant term to the right: Add '-4.071428571' to each side of the equation. 4.071428571 + -5.714285714x + -4.071428571 + x2 = 0 + -4.071428571 Reorder the terms: 4.071428571 + -4.071428571 + -5.714285714x + x2 = 0 + -4.071428571 Combine like terms: 4.071428571 + -4.071428571 = 0.000000000 0.000000000 + -5.714285714x + x2 = 0 + -4.071428571 -5.714285714x + x2 = 0 + -4.071428571 Combine like terms: 0 + -4.071428571 = -4.071428571 -5.714285714x + x2 = -4.071428571 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 = -4.071428571 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714x + x2 = -4.071428571 + 8.163265305 Combine like terms: -4.071428571 + 8.163265305 = 4.091836734 8.163265305 + -5.714285714x + x2 = 4.091836734 Factor a perfect square on the left side: (x + -2.857142857)(x + -2.857142857) = 4.091836734 Calculate the square root of the right side: 2.022828894 Break this problem into two subproblems by setting (x + -2.857142857) equal to 2.022828894 and -2.022828894.Subproblem 1
x + -2.857142857 = 2.022828894 Simplifying x + -2.857142857 = 2.022828894 Reorder the terms: -2.857142857 + x = 2.022828894 Solving -2.857142857 + x = 2.022828894 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 = 2.022828894 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = 2.022828894 + 2.857142857 x = 2.022828894 + 2.857142857 Combine like terms: 2.022828894 + 2.857142857 = 4.879971751 x = 4.879971751 Simplifying x = 4.879971751Subproblem 2
x + -2.857142857 = -2.022828894 Simplifying x + -2.857142857 = -2.022828894 Reorder the terms: -2.857142857 + x = -2.022828894 Solving -2.857142857 + x = -2.022828894 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 = -2.022828894 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = -2.022828894 + 2.857142857 x = -2.022828894 + 2.857142857 Combine like terms: -2.022828894 + 2.857142857 = 0.834313963 x = 0.834313963 Simplifying x = 0.834313963Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.879971751, 0.834313963}
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