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Simplifying x2 + 92x + -109 = 0 Reorder the terms: -109 + 92x + x2 = 0 Solving -109 + 92x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '109' to each side of the equation. -109 + 92x + 109 + x2 = 0 + 109 Reorder the terms: -109 + 109 + 92x + x2 = 0 + 109 Combine like terms: -109 + 109 = 0 0 + 92x + x2 = 0 + 109 92x + x2 = 0 + 109 Combine like terms: 0 + 109 = 109 92x + x2 = 109 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 = 109 + 2116 Reorder the terms: 2116 + 92x + x2 = 109 + 2116 Combine like terms: 109 + 2116 = 2225 2116 + 92x + x2 = 2225 Factor a perfect square on the left side: (x + 46)(x + 46) = 2225 Calculate the square root of the right side: 47.16990566 Break this problem into two subproblems by setting (x + 46) equal to 47.16990566 and -47.16990566.Subproblem 1
x + 46 = 47.16990566 Simplifying x + 46 = 47.16990566 Reorder the terms: 46 + x = 47.16990566 Solving 46 + x = 47.16990566 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 = 47.16990566 + -46 Combine like terms: 46 + -46 = 0 0 + x = 47.16990566 + -46 x = 47.16990566 + -46 Combine like terms: 47.16990566 + -46 = 1.16990566 x = 1.16990566 Simplifying x = 1.16990566Subproblem 2
x + 46 = -47.16990566 Simplifying x + 46 = -47.16990566 Reorder the terms: 46 + x = -47.16990566 Solving 46 + x = -47.16990566 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 = -47.16990566 + -46 Combine like terms: 46 + -46 = 0 0 + x = -47.16990566 + -46 x = -47.16990566 + -46 Combine like terms: -47.16990566 + -46 = -93.16990566 x = -93.16990566 Simplifying x = -93.16990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16990566, -93.16990566}
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