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Simplifying x2 + -7x + 1.2 = 0 Reorder the terms: 1.2 + -7x + x2 = 0 Solving 1.2 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -7x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -7x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -7x + x2 = 0 + -1.2 -7x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -7x + x2 = -1.2 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1.2 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.2 + 12.25 Combine like terms: -1.2 + 12.25 = 11.05 12.25 + -7x + x2 = 11.05 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.05 Calculate the square root of the right side: 3.324154028 Break this problem into two subproblems by setting (x + -3.5) equal to 3.324154028 and -3.324154028.Subproblem 1
x + -3.5 = 3.324154028 Simplifying x + -3.5 = 3.324154028 Reorder the terms: -3.5 + x = 3.324154028 Solving -3.5 + x = 3.324154028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.324154028 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.324154028 + 3.5 x = 3.324154028 + 3.5 Combine like terms: 3.324154028 + 3.5 = 6.824154028 x = 6.824154028 Simplifying x = 6.824154028Subproblem 2
x + -3.5 = -3.324154028 Simplifying x + -3.5 = -3.324154028 Reorder the terms: -3.5 + x = -3.324154028 Solving -3.5 + x = -3.324154028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.324154028 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.324154028 + 3.5 x = -3.324154028 + 3.5 Combine like terms: -3.324154028 + 3.5 = 0.175845972 x = 0.175845972 Simplifying x = 0.175845972Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.824154028, 0.175845972}
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