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Simplifying x2 + 2.1x + -1610.9 = 0 Reorder the terms: -1610.9 + 2.1x + x2 = 0 Solving -1610.9 + 2.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1610.9' to each side of the equation. -1610.9 + 2.1x + 1610.9 + x2 = 0 + 1610.9 Reorder the terms: -1610.9 + 1610.9 + 2.1x + x2 = 0 + 1610.9 Combine like terms: -1610.9 + 1610.9 = 0.0 0.0 + 2.1x + x2 = 0 + 1610.9 2.1x + x2 = 0 + 1610.9 Combine like terms: 0 + 1610.9 = 1610.9 2.1x + x2 = 1610.9 The x term is 2.1x. Take half its coefficient (1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. 2.1x + 1.1025 + x2 = 1610.9 + 1.1025 Reorder the terms: 1.1025 + 2.1x + x2 = 1610.9 + 1.1025 Combine like terms: 1610.9 + 1.1025 = 1612.0025 1.1025 + 2.1x + x2 = 1612.0025 Factor a perfect square on the left side: (x + 1.05)(x + 1.05) = 1612.0025 Calculate the square root of the right side: 40.149750933 Break this problem into two subproblems by setting (x + 1.05) equal to 40.149750933 and -40.149750933.Subproblem 1
x + 1.05 = 40.149750933 Simplifying x + 1.05 = 40.149750933 Reorder the terms: 1.05 + x = 40.149750933 Solving 1.05 + x = 40.149750933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = 40.149750933 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = 40.149750933 + -1.05 x = 40.149750933 + -1.05 Combine like terms: 40.149750933 + -1.05 = 39.099750933 x = 39.099750933 Simplifying x = 39.099750933Subproblem 2
x + 1.05 = -40.149750933 Simplifying x + 1.05 = -40.149750933 Reorder the terms: 1.05 + x = -40.149750933 Solving 1.05 + x = -40.149750933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = -40.149750933 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = -40.149750933 + -1.05 x = -40.149750933 + -1.05 Combine like terms: -40.149750933 + -1.05 = -41.199750933 x = -41.199750933 Simplifying x = -41.199750933Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.099750933, -41.199750933}
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