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Simplifying 17x2 + -77x + 24 = 0 Reorder the terms: 24 + -77x + 17x2 = 0 Solving 24 + -77x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 1.411764706 + -4.529411765x + x2 = 0 Move the constant term to the right: Add '-1.411764706' to each side of the equation. 1.411764706 + -4.529411765x + -1.411764706 + x2 = 0 + -1.411764706 Reorder the terms: 1.411764706 + -1.411764706 + -4.529411765x + x2 = 0 + -1.411764706 Combine like terms: 1.411764706 + -1.411764706 = 0.000000000 0.000000000 + -4.529411765x + x2 = 0 + -1.411764706 -4.529411765x + x2 = 0 + -1.411764706 Combine like terms: 0 + -1.411764706 = -1.411764706 -4.529411765x + x2 = -1.411764706 The x term is -4.529411765x. Take half its coefficient (-2.264705883). Square it (5.128892736) and add it to both sides. Add '5.128892736' to each side of the equation. -4.529411765x + 5.128892736 + x2 = -1.411764706 + 5.128892736 Reorder the terms: 5.128892736 + -4.529411765x + x2 = -1.411764706 + 5.128892736 Combine like terms: -1.411764706 + 5.128892736 = 3.71712803 5.128892736 + -4.529411765x + x2 = 3.71712803 Factor a perfect square on the left side: (x + -2.264705883)(x + -2.264705883) = 3.71712803 Calculate the square root of the right side: 1.927985485 Break this problem into two subproblems by setting (x + -2.264705883) equal to 1.927985485 and -1.927985485.Subproblem 1
x + -2.264705883 = 1.927985485 Simplifying x + -2.264705883 = 1.927985485 Reorder the terms: -2.264705883 + x = 1.927985485 Solving -2.264705883 + x = 1.927985485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.264705883' to each side of the equation. -2.264705883 + 2.264705883 + x = 1.927985485 + 2.264705883 Combine like terms: -2.264705883 + 2.264705883 = 0.000000000 0.000000000 + x = 1.927985485 + 2.264705883 x = 1.927985485 + 2.264705883 Combine like terms: 1.927985485 + 2.264705883 = 4.192691368 x = 4.192691368 Simplifying x = 4.192691368Subproblem 2
x + -2.264705883 = -1.927985485 Simplifying x + -2.264705883 = -1.927985485 Reorder the terms: -2.264705883 + x = -1.927985485 Solving -2.264705883 + x = -1.927985485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.264705883' to each side of the equation. -2.264705883 + 2.264705883 + x = -1.927985485 + 2.264705883 Combine like terms: -2.264705883 + 2.264705883 = 0.000000000 0.000000000 + x = -1.927985485 + 2.264705883 x = -1.927985485 + 2.264705883 Combine like terms: -1.927985485 + 2.264705883 = 0.336720398 x = 0.336720398 Simplifying x = 0.336720398Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.192691368, 0.336720398}
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