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Simplifying x2 + -1x + -106 = 0 Reorder the terms: -106 + -1x + x2 = 0 Solving -106 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '106' to each side of the equation. -106 + -1x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + -1x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + -1x + x2 = 0 + 106 -1x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 -1x + x2 = 106 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 106 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 106 + 0.25 Combine like terms: 106 + 0.25 = 106.25 0.25 + -1x + x2 = 106.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -0.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -0.5 = 10.307764064 Simplifying x + -0.5 = 10.307764064 Reorder the terms: -0.5 + x = 10.307764064 Solving -0.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 10.307764064 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 10.307764064 + 0.5 x = 10.307764064 + 0.5 Combine like terms: 10.307764064 + 0.5 = 10.807764064 x = 10.807764064 Simplifying x = 10.807764064Subproblem 2
x + -0.5 = -10.307764064 Simplifying x + -0.5 = -10.307764064 Reorder the terms: -0.5 + x = -10.307764064 Solving -0.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -10.307764064 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -10.307764064 + 0.5 x = -10.307764064 + 0.5 Combine like terms: -10.307764064 + 0.5 = -9.807764064 x = -9.807764064 Simplifying x = -9.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.807764064, -9.807764064}
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