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Simplifying x2 + -2x + -22.5 = 0 Reorder the terms: -22.5 + -2x + x2 = 0 Solving -22.5 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -2x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -2x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -2x + x2 = 0 + 22.5 -2x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -2x + x2 = 22.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 22.5 + 1 Reorder the terms: 1 + -2x + x2 = 22.5 + 1 Combine like terms: 22.5 + 1 = 23.5 1 + -2x + x2 = 23.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (x + -1) equal to 4.847679857 and -4.847679857.Subproblem 1
x + -1 = 4.847679857 Simplifying x + -1 = 4.847679857 Reorder the terms: -1 + x = 4.847679857 Solving -1 + x = 4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.847679857 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.847679857 + 1 x = 4.847679857 + 1 Combine like terms: 4.847679857 + 1 = 5.847679857 x = 5.847679857 Simplifying x = 5.847679857Subproblem 2
x + -1 = -4.847679857 Simplifying x + -1 = -4.847679857 Reorder the terms: -1 + x = -4.847679857 Solving -1 + x = -4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.847679857 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.847679857 + 1 x = -4.847679857 + 1 Combine like terms: -4.847679857 + 1 = -3.847679857 x = -3.847679857 Simplifying x = -3.847679857Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.847679857, -3.847679857}
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