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Simplifying 225 = x2 + -2x Reorder the terms: 225 = -2x + x2 Solving 225 = -2x + x2 Solving for variable 'x'. Reorder the terms: 225 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 225 + 2x + -1x2 = 0 + x2 + -1x2 225 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 225 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -225 + -2x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + -2x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + -2x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + -2x + x2 = 0 + 225 -2x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 -2x + x2 = 225 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 = 225 + 1 Reorder the terms: 1 + -2x + x2 = 225 + 1 Combine like terms: 225 + 1 = 226 1 + -2x + x2 = 226 Factor a perfect square on the left side: (x + -1)(x + -1) = 226 Calculate the square root of the right side: 15.033296378 Break this problem into two subproblems by setting (x + -1) equal to 15.033296378 and -15.033296378.Subproblem 1
x + -1 = 15.033296378 Simplifying x + -1 = 15.033296378 Reorder the terms: -1 + x = 15.033296378 Solving -1 + x = 15.033296378 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 = 15.033296378 + 1 Combine like terms: -1 + 1 = 0 0 + x = 15.033296378 + 1 x = 15.033296378 + 1 Combine like terms: 15.033296378 + 1 = 16.033296378 x = 16.033296378 Simplifying x = 16.033296378Subproblem 2
x + -1 = -15.033296378 Simplifying x + -1 = -15.033296378 Reorder the terms: -1 + x = -15.033296378 Solving -1 + x = -15.033296378 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 = -15.033296378 + 1 Combine like terms: -1 + 1 = 0 0 + x = -15.033296378 + 1 x = -15.033296378 + 1 Combine like terms: -15.033296378 + 1 = -14.033296378 x = -14.033296378 Simplifying x = -14.033296378Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.033296378, -14.033296378}
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