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Simplifying x2 + 92x + -432 = 0 Reorder the terms: -432 + 92x + x2 = 0 Solving -432 + 92x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '432' to each side of the equation. -432 + 92x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + 92x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + 92x + x2 = 0 + 432 92x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 92x + x2 = 432 The x term is 92x. Take half its coefficient (46). Square it (2116) and add it to both sides. Add '2116' to each side of the equation. 92x + 2116 + x2 = 432 + 2116 Reorder the terms: 2116 + 92x + x2 = 432 + 2116 Combine like terms: 432 + 2116 = 2548 2116 + 92x + x2 = 2548 Factor a perfect square on the left side: (x + 46)(x + 46) = 2548 Calculate the square root of the right side: 50.477717856 Break this problem into two subproblems by setting (x + 46) equal to 50.477717856 and -50.477717856.Subproblem 1
x + 46 = 50.477717856 Simplifying x + 46 = 50.477717856 Reorder the terms: 46 + x = 50.477717856 Solving 46 + x = 50.477717856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = 50.477717856 + -46 Combine like terms: 46 + -46 = 0 0 + x = 50.477717856 + -46 x = 50.477717856 + -46 Combine like terms: 50.477717856 + -46 = 4.477717856 x = 4.477717856 Simplifying x = 4.477717856Subproblem 2
x + 46 = -50.477717856 Simplifying x + 46 = -50.477717856 Reorder the terms: 46 + x = -50.477717856 Solving 46 + x = -50.477717856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = -50.477717856 + -46 Combine like terms: 46 + -46 = 0 0 + x = -50.477717856 + -46 x = -50.477717856 + -46 Combine like terms: -50.477717856 + -46 = -96.477717856 x = -96.477717856 Simplifying x = -96.477717856Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.477717856, -96.477717856}
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