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Simplifying x2 + -4x + -4 = 2.5 + 4 Reorder the terms: -4 + -4x + x2 = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 -4 + -4x + x2 = 6.5 Solving -4 + -4x + x2 = 6.5 Solving for variable 'x'. Reorder the terms: -4 + -6.5 + -4x + x2 = 6.5 + -6.5 Combine like terms: -4 + -6.5 = -10.5 -10.5 + -4x + x2 = 6.5 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 -10.5 + -4x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -4x + 10.5 + x2 = 0.0 + 10.5 Reorder the terms: -10.5 + 10.5 + -4x + x2 = 0.0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -4x + x2 = 0.0 + 10.5 -4x + x2 = 0.0 + 10.5 Combine like terms: 0.0 + 10.5 = 10.5 -4x + x2 = 10.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 10.5 + 4 Reorder the terms: 4 + -4x + x2 = 10.5 + 4 Combine like terms: 10.5 + 4 = 14.5 4 + -4x + x2 = 14.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (x + -2) equal to 3.807886553 and -3.807886553.Subproblem 1
x + -2 = 3.807886553 Simplifying x + -2 = 3.807886553 Reorder the terms: -2 + x = 3.807886553 Solving -2 + x = 3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.807886553 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.807886553 + 2 x = 3.807886553 + 2 Combine like terms: 3.807886553 + 2 = 5.807886553 x = 5.807886553 Simplifying x = 5.807886553Subproblem 2
x + -2 = -3.807886553 Simplifying x + -2 = -3.807886553 Reorder the terms: -2 + x = -3.807886553 Solving -2 + x = -3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.807886553 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.807886553 + 2 x = -3.807886553 + 2 Combine like terms: -3.807886553 + 2 = -1.807886553 x = -1.807886553 Simplifying x = -1.807886553Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.807886553, -1.807886553}
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