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Simplifying x2 + 41x = 12 Reorder the terms: 41x + x2 = 12 Solving 41x + x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 41x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 41x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 41x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 41x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 41x + x2 = 0 + 12 41x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 41x + x2 = 12 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = 12 + 420.25 Reorder the terms: 420.25 + 41x + x2 = 12 + 420.25 Combine like terms: 12 + 420.25 = 432.25 420.25 + 41x + x2 = 432.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 432.25 Calculate the square root of the right side: 20.790622886 Break this problem into two subproblems by setting (x + 20.5) equal to 20.790622886 and -20.790622886.Subproblem 1
x + 20.5 = 20.790622886 Simplifying x + 20.5 = 20.790622886 Reorder the terms: 20.5 + x = 20.790622886 Solving 20.5 + x = 20.790622886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 20.790622886 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 20.790622886 + -20.5 x = 20.790622886 + -20.5 Combine like terms: 20.790622886 + -20.5 = 0.290622886 x = 0.290622886 Simplifying x = 0.290622886Subproblem 2
x + 20.5 = -20.790622886 Simplifying x + 20.5 = -20.790622886 Reorder the terms: 20.5 + x = -20.790622886 Solving 20.5 + x = -20.790622886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -20.790622886 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -20.790622886 + -20.5 x = -20.790622886 + -20.5 Combine like terms: -20.790622886 + -20.5 = -41.290622886 x = -41.290622886 Simplifying x = -41.290622886Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.290622886, -41.290622886}
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