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Simplifying 7X2 + 22X + -16 = 0 Reorder the terms: -16 + 22X + 7X2 = 0 Solving -16 + 22X + 7X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 3.142857143X + X2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 3.142857143X + 2.285714286 + X2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 3.142857143X + X2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 3.142857143X + X2 = 0 + 2.285714286 3.142857143X + X2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 3.142857143X + X2 = 2.285714286 The X term is 3.142857143X. Take half its coefficient (1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. 3.142857143X + 2.469387757 + X2 = 2.285714286 + 2.469387757 Reorder the terms: 2.469387757 + 3.142857143X + X2 = 2.285714286 + 2.469387757 Combine like terms: 2.285714286 + 2.469387757 = 4.755102043 2.469387757 + 3.142857143X + X2 = 4.755102043 Factor a perfect square on the left side: (X + 1.571428572)(X + 1.571428572) = 4.755102043 Calculate the square root of the right side: 2.180619647 Break this problem into two subproblems by setting (X + 1.571428572) equal to 2.180619647 and -2.180619647.Subproblem 1
X + 1.571428572 = 2.180619647 Simplifying X + 1.571428572 = 2.180619647 Reorder the terms: 1.571428572 + X = 2.180619647 Solving 1.571428572 + X = 2.180619647 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + X = 2.180619647 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + X = 2.180619647 + -1.571428572 X = 2.180619647 + -1.571428572 Combine like terms: 2.180619647 + -1.571428572 = 0.609191075 X = 0.609191075 Simplifying X = 0.609191075Subproblem 2
X + 1.571428572 = -2.180619647 Simplifying X + 1.571428572 = -2.180619647 Reorder the terms: 1.571428572 + X = -2.180619647 Solving 1.571428572 + X = -2.180619647 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + X = -2.180619647 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + X = -2.180619647 + -1.571428572 X = -2.180619647 + -1.571428572 Combine like terms: -2.180619647 + -1.571428572 = -3.752048219 X = -3.752048219 Simplifying X = -3.752048219Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.609191075, -3.752048219}
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