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Simplifying 40 = x2 + x Reorder the terms: 40 = x + x2 Solving 40 = x + x2 Solving for variable 'x'. Reorder the terms: 40 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 40 + -1x + -1x2 = 0 + x2 + -1x2 40 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + x + x2 = 0 + 40 x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 x + x2 = 40 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 40 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 1.25 + x2 = 40.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 0.5 = 6.34428877 Simplifying x + 0.5 = 6.34428877 Reorder the terms: 0.5 + x = 6.34428877 Solving 0.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.34428877 + -0.5 x = 6.34428877 + -0.5 Combine like terms: 6.34428877 + -0.5 = 5.84428877 x = 5.84428877 Simplifying x = 5.84428877Subproblem 2
x + 0.5 = -6.34428877 Simplifying x + 0.5 = -6.34428877 Reorder the terms: 0.5 + x = -6.34428877 Solving 0.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.34428877 + -0.5 x = -6.34428877 + -0.5 Combine like terms: -6.34428877 + -0.5 = -6.84428877 x = -6.84428877 Simplifying x = -6.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.84428877, -6.84428877}
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