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Simplifying x2 + -0.666x = 7 Reorder the terms: -0.666x + x2 = 7 Solving -0.666x + x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -0.666x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -0.666x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.666x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.666x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.666x + x2 = 0 + 7 -0.666x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.666x + x2 = 7 The x term is -0.666x. Take half its coefficient (-0.333). Square it (0.110889) and add it to both sides. Add '0.110889' to each side of the equation. -0.666x + 0.110889 + x2 = 7 + 0.110889 Reorder the terms: 0.110889 + -0.666x + x2 = 7 + 0.110889 Combine like terms: 7 + 0.110889 = 7.110889 0.110889 + -0.666x + x2 = 7.110889 Factor a perfect square on the left side: (x + -0.333)(x + -0.333) = 7.110889 Calculate the square root of the right side: 2.666625021 Break this problem into two subproblems by setting (x + -0.333) equal to 2.666625021 and -2.666625021.Subproblem 1
x + -0.333 = 2.666625021 Simplifying x + -0.333 = 2.666625021 Reorder the terms: -0.333 + x = 2.666625021 Solving -0.333 + x = 2.666625021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.333' to each side of the equation. -0.333 + 0.333 + x = 2.666625021 + 0.333 Combine like terms: -0.333 + 0.333 = 0.000 0.000 + x = 2.666625021 + 0.333 x = 2.666625021 + 0.333 Combine like terms: 2.666625021 + 0.333 = 2.999625021 x = 2.999625021 Simplifying x = 2.999625021Subproblem 2
x + -0.333 = -2.666625021 Simplifying x + -0.333 = -2.666625021 Reorder the terms: -0.333 + x = -2.666625021 Solving -0.333 + x = -2.666625021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.333' to each side of the equation. -0.333 + 0.333 + x = -2.666625021 + 0.333 Combine like terms: -0.333 + 0.333 = 0.000 0.000 + x = -2.666625021 + 0.333 x = -2.666625021 + 0.333 Combine like terms: -2.666625021 + 0.333 = -2.333625021 x = -2.333625021 Simplifying x = -2.333625021Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.999625021, -2.333625021}
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