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Simplifying 0.875x2 + -3.25x + 0.5 = 0.375x Reorder the terms: 0.5 + -3.25x + 0.875x2 = 0.375x Solving 0.5 + -3.25x + 0.875x2 = 0.375x Solving for variable 'x'. Reorder the terms: 0.5 + -3.25x + -0.375x + 0.875x2 = 0.375x + -0.375x Combine like terms: -3.25x + -0.375x = -3.625x 0.5 + -3.625x + 0.875x2 = 0.375x + -0.375x Combine like terms: 0.375x + -0.375x = 0.000 0.5 + -3.625x + 0.875x2 = 0.000 Begin completing the square. Divide all terms by 0.875 the coefficient of the squared term: Divide each side by '0.875'. 0.5714285714 + -4.142857143x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -4.142857143x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -4.142857143x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -4.142857143x + x2 = 0 + -0.5714285714 -4.142857143x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -4.142857143x + x2 = -0.5714285714 The x term is -4.142857143x. Take half its coefficient (-2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. -4.142857143x + 4.290816329 + x2 = -0.5714285714 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143x + x2 = -0.5714285714 + 4.290816329 Combine like terms: -0.5714285714 + 4.290816329 = 3.7193877576 4.290816329 + -4.142857143x + x2 = 3.7193877576 Factor a perfect square on the left side: (x + -2.071428572)(x + -2.071428572) = 3.7193877576 Calculate the square root of the right side: 1.928571429 Break this problem into two subproblems by setting (x + -2.071428572) equal to 1.928571429 and -1.928571429.Subproblem 1
x + -2.071428572 = 1.928571429 Simplifying x + -2.071428572 = 1.928571429 Reorder the terms: -2.071428572 + x = 1.928571429 Solving -2.071428572 + x = 1.928571429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = 1.928571429 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = 1.928571429 + 2.071428572 x = 1.928571429 + 2.071428572 Combine like terms: 1.928571429 + 2.071428572 = 4.000000001 x = 4.000000001 Simplifying x = 4.000000001Subproblem 2
x + -2.071428572 = -1.928571429 Simplifying x + -2.071428572 = -1.928571429 Reorder the terms: -2.071428572 + x = -1.928571429 Solving -2.071428572 + x = -1.928571429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = -1.928571429 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = -1.928571429 + 2.071428572 x = -1.928571429 + 2.071428572 Combine like terms: -1.928571429 + 2.071428572 = 0.142857143 x = 0.142857143 Simplifying x = 0.142857143Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.000000001, 0.142857143}
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