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Simplifying x2 + 3x + -833 = 0 Reorder the terms: -833 + 3x + x2 = 0 Solving -833 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '833' to each side of the equation. -833 + 3x + 833 + x2 = 0 + 833 Reorder the terms: -833 + 833 + 3x + x2 = 0 + 833 Combine like terms: -833 + 833 = 0 0 + 3x + x2 = 0 + 833 3x + x2 = 0 + 833 Combine like terms: 0 + 833 = 833 3x + x2 = 833 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 = 833 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 833 + 2.25 Combine like terms: 833 + 2.25 = 835.25 2.25 + 3x + x2 = 835.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 835.25 Calculate the square root of the right side: 28.900692033 Break this problem into two subproblems by setting (x + 1.5) equal to 28.900692033 and -28.900692033.Subproblem 1
x + 1.5 = 28.900692033 Simplifying x + 1.5 = 28.900692033 Reorder the terms: 1.5 + x = 28.900692033 Solving 1.5 + x = 28.900692033 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 = 28.900692033 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 28.900692033 + -1.5 x = 28.900692033 + -1.5 Combine like terms: 28.900692033 + -1.5 = 27.400692033 x = 27.400692033 Simplifying x = 27.400692033Subproblem 2
x + 1.5 = -28.900692033 Simplifying x + 1.5 = -28.900692033 Reorder the terms: 1.5 + x = -28.900692033 Solving 1.5 + x = -28.900692033 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 = -28.900692033 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -28.900692033 + -1.5 x = -28.900692033 + -1.5 Combine like terms: -28.900692033 + -1.5 = -30.400692033 x = -30.400692033 Simplifying x = -30.400692033Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.400692033, -30.400692033}
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