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Simplifying 3x + x2 = 83 Solving 3x + x2 = 83 Solving for variable 'x'. Reorder the terms: -83 + 3x + x2 = 83 + -83 Combine like terms: 83 + -83 = 0 -83 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + 3x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + 3x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + 3x + x2 = 0 + 83 3x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 3x + x2 = 83 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 = 83 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 83 + 2.25 Combine like terms: 83 + 2.25 = 85.25 2.25 + 3x + x2 = 85.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + 1.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + 1.5 = 9.233092656 Simplifying x + 1.5 = 9.233092656 Reorder the terms: 1.5 + x = 9.233092656 Solving 1.5 + x = 9.233092656 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 = 9.233092656 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.233092656 + -1.5 x = 9.233092656 + -1.5 Combine like terms: 9.233092656 + -1.5 = 7.733092656 x = 7.733092656 Simplifying x = 7.733092656Subproblem 2
x + 1.5 = -9.233092656 Simplifying x + 1.5 = -9.233092656 Reorder the terms: 1.5 + x = -9.233092656 Solving 1.5 + x = -9.233092656 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 = -9.233092656 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.233092656 + -1.5 x = -9.233092656 + -1.5 Combine like terms: -9.233092656 + -1.5 = -10.733092656 x = -10.733092656 Simplifying x = -10.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.733092656, -10.733092656}
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