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Simplifying 15 = x2 + 2x + 2 Reorder the terms: 15 = 2 + 2x + x2 Solving 15 = 2 + 2x + x2 Solving for variable 'x'. Combine like terms: 15 + -2 = 13 13 + -2x + -1x2 = 2 + 2x + x2 + -2 + -2x + -1x2 Reorder the terms: 13 + -2x + -1x2 = 2 + -2 + 2x + -2x + x2 + -1x2 Combine like terms: 2 + -2 = 0 13 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 13 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 13 + -2x + -1x2 = 0 + x2 + -1x2 13 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 13 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 2x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 2x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 2x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2x + x2 = 0 + 13 2x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 2x + x2 = 13 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 = 13 + 1 Reorder the terms: 1 + 2x + x2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2x + x2 = 14 Factor a perfect square on the left side: (x + 1)(x + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 1 = 3.741657387 Simplifying x + 1 = 3.741657387 Reorder the terms: 1 + x = 3.741657387 Solving 1 + x = 3.741657387 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 = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.741657387 + -1 x = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 x = 2.741657387 Simplifying x = 2.741657387Subproblem 2
x + 1 = -3.741657387 Simplifying x + 1 = -3.741657387 Reorder the terms: 1 + x = -3.741657387 Solving 1 + x = -3.741657387 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 = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.741657387 + -1 x = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 x = -4.741657387 Simplifying x = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.741657387, -4.741657387}
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