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Simplifying 40 = x2 + 2x Reorder the terms: 40 = 2x + x2 Solving 40 = 2x + x2 Solving for variable 'x'. Reorder the terms: 40 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 40 + -2x + -1x2 = 0 + x2 + -1x2 40 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 2x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 2x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 2x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 2x + x2 = 0 + 40 2x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 2x + x2 = 40 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 = 40 + 1 Reorder the terms: 1 + 2x + x2 = 40 + 1 Combine like terms: 40 + 1 = 41 1 + 2x + x2 = 41 Factor a perfect square on the left side: (x + 1)(x + 1) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 1) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 1 = 6.403124237 Simplifying x + 1 = 6.403124237 Reorder the terms: 1 + x = 6.403124237 Solving 1 + x = 6.403124237 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 = 6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.403124237 + -1 x = 6.403124237 + -1 Combine like terms: 6.403124237 + -1 = 5.403124237 x = 5.403124237 Simplifying x = 5.403124237Subproblem 2
x + 1 = -6.403124237 Simplifying x + 1 = -6.403124237 Reorder the terms: 1 + x = -6.403124237 Solving 1 + x = -6.403124237 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 = -6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.403124237 + -1 x = -6.403124237 + -1 Combine like terms: -6.403124237 + -1 = -7.403124237 x = -7.403124237 Simplifying x = -7.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.403124237, -7.403124237}
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