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Simplifying x2 + 3x = 81 Reorder the terms: 3x + x2 = 81 Solving 3x + x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + 3x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 3x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 3x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 3x + x2 = 0 + 81 3x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 3x + x2 = 81 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 81 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 81 + 2.25 Combine like terms: 81 + 2.25 = 83.25 2.25 + 3x + x2 = 83.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (x + 1.5) equal to 9.124143795 and -9.124143795.Subproblem 1
x + 1.5 = 9.124143795 Simplifying x + 1.5 = 9.124143795 Reorder the terms: 1.5 + x = 9.124143795 Solving 1.5 + x = 9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.124143795 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.124143795 + -1.5 x = 9.124143795 + -1.5 Combine like terms: 9.124143795 + -1.5 = 7.624143795 x = 7.624143795 Simplifying x = 7.624143795Subproblem 2
x + 1.5 = -9.124143795 Simplifying x + 1.5 = -9.124143795 Reorder the terms: 1.5 + x = -9.124143795 Solving 1.5 + x = -9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.124143795 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.124143795 + -1.5 x = -9.124143795 + -1.5 Combine like terms: -9.124143795 + -1.5 = -10.624143795 x = -10.624143795 Simplifying x = -10.624143795Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.624143795, -10.624143795}
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