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Simplifying x2 + -4x + -27.25 = 0 Reorder the terms: -27.25 + -4x + x2 = 0 Solving -27.25 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27.25' to each side of the equation. -27.25 + -4x + 27.25 + x2 = 0 + 27.25 Reorder the terms: -27.25 + 27.25 + -4x + x2 = 0 + 27.25 Combine like terms: -27.25 + 27.25 = 0.00 0.00 + -4x + x2 = 0 + 27.25 -4x + x2 = 0 + 27.25 Combine like terms: 0 + 27.25 = 27.25 -4x + x2 = 27.25 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 = 27.25 + 4 Reorder the terms: 4 + -4x + x2 = 27.25 + 4 Combine like terms: 27.25 + 4 = 31.25 4 + -4x + x2 = 31.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -2) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -2 = 5.590169944 Simplifying x + -2 = 5.590169944 Reorder the terms: -2 + x = 5.590169944 Solving -2 + x = 5.590169944 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 = 5.590169944 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.590169944 + 2 x = 5.590169944 + 2 Combine like terms: 5.590169944 + 2 = 7.590169944 x = 7.590169944 Simplifying x = 7.590169944Subproblem 2
x + -2 = -5.590169944 Simplifying x + -2 = -5.590169944 Reorder the terms: -2 + x = -5.590169944 Solving -2 + x = -5.590169944 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 = -5.590169944 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.590169944 + 2 x = -5.590169944 + 2 Combine like terms: -5.590169944 + 2 = -3.590169944 x = -3.590169944 Simplifying x = -3.590169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.590169944, -3.590169944}
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