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Simplifying x2 + 3x = 212 Reorder the terms: 3x + x2 = 212 Solving 3x + x2 = 212 Solving for variable 'x'. Reorder the terms: -212 + 3x + x2 = 212 + -212 Combine like terms: 212 + -212 = 0 -212 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '212' to each side of the equation. -212 + 3x + 212 + x2 = 0 + 212 Reorder the terms: -212 + 212 + 3x + x2 = 0 + 212 Combine like terms: -212 + 212 = 0 0 + 3x + x2 = 0 + 212 3x + x2 = 0 + 212 Combine like terms: 0 + 212 = 212 3x + x2 = 212 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 = 212 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 212 + 2.25 Combine like terms: 212 + 2.25 = 214.25 2.25 + 3x + x2 = 214.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 214.25 Calculate the square root of the right side: 14.637281168 Break this problem into two subproblems by setting (x + 1.5) equal to 14.637281168 and -14.637281168.Subproblem 1
x + 1.5 = 14.637281168 Simplifying x + 1.5 = 14.637281168 Reorder the terms: 1.5 + x = 14.637281168 Solving 1.5 + x = 14.637281168 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 = 14.637281168 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.637281168 + -1.5 x = 14.637281168 + -1.5 Combine like terms: 14.637281168 + -1.5 = 13.137281168 x = 13.137281168 Simplifying x = 13.137281168Subproblem 2
x + 1.5 = -14.637281168 Simplifying x + 1.5 = -14.637281168 Reorder the terms: 1.5 + x = -14.637281168 Solving 1.5 + x = -14.637281168 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 = -14.637281168 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.637281168 + -1.5 x = -14.637281168 + -1.5 Combine like terms: -14.637281168 + -1.5 = -16.137281168 x = -16.137281168 Simplifying x = -16.137281168Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.137281168, -16.137281168}
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