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Simplifying x2 + 3x = 2187 Reorder the terms: 3x + x2 = 2187 Solving 3x + x2 = 2187 Solving for variable 'x'. Reorder the terms: -2187 + 3x + x2 = 2187 + -2187 Combine like terms: 2187 + -2187 = 0 -2187 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2187' to each side of the equation. -2187 + 3x + 2187 + x2 = 0 + 2187 Reorder the terms: -2187 + 2187 + 3x + x2 = 0 + 2187 Combine like terms: -2187 + 2187 = 0 0 + 3x + x2 = 0 + 2187 3x + x2 = 0 + 2187 Combine like terms: 0 + 2187 = 2187 3x + x2 = 2187 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 = 2187 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2187 + 2.25 Combine like terms: 2187 + 2.25 = 2189.25 2.25 + 3x + x2 = 2189.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2189.25 Calculate the square root of the right side: 46.789421881 Break this problem into two subproblems by setting (x + 1.5) equal to 46.789421881 and -46.789421881.Subproblem 1
x + 1.5 = 46.789421881 Simplifying x + 1.5 = 46.789421881 Reorder the terms: 1.5 + x = 46.789421881 Solving 1.5 + x = 46.789421881 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 = 46.789421881 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 46.789421881 + -1.5 x = 46.789421881 + -1.5 Combine like terms: 46.789421881 + -1.5 = 45.289421881 x = 45.289421881 Simplifying x = 45.289421881Subproblem 2
x + 1.5 = -46.789421881 Simplifying x + 1.5 = -46.789421881 Reorder the terms: 1.5 + x = -46.789421881 Solving 1.5 + x = -46.789421881 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 = -46.789421881 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -46.789421881 + -1.5 x = -46.789421881 + -1.5 Combine like terms: -46.789421881 + -1.5 = -48.289421881 x = -48.289421881 Simplifying x = -48.289421881Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.289421881, -48.289421881}
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