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Simplifying 97.8061x2 + -5x + -105 = 0 Reorder the terms: -105 + -5x + 97.8061x2 = 0 Solving -105 + -5x + 97.8061x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 97.8061 the coefficient of the squared term: Divide each side by '97.8061'. -1.073552672 + -0.05112155581x + x2 = 0 Move the constant term to the right: Add '1.073552672' to each side of the equation. -1.073552672 + -0.05112155581x + 1.073552672 + x2 = 0 + 1.073552672 Reorder the terms: -1.073552672 + 1.073552672 + -0.05112155581x + x2 = 0 + 1.073552672 Combine like terms: -1.073552672 + 1.073552672 = 0.000000000 0.000000000 + -0.05112155581x + x2 = 0 + 1.073552672 -0.05112155581x + x2 = 0 + 1.073552672 Combine like terms: 0 + 1.073552672 = 1.073552672 -0.05112155581x + x2 = 1.073552672 The x term is -0.05112155581x. Take half its coefficient (-0.02556077791). Square it (0.0006533533674) and add it to both sides. Add '0.0006533533674' to each side of the equation. -0.05112155581x + 0.0006533533674 + x2 = 1.073552672 + 0.0006533533674 Reorder the terms: 0.0006533533674 + -0.05112155581x + x2 = 1.073552672 + 0.0006533533674 Combine like terms: 1.073552672 + 0.0006533533674 = 1.0742060253674 0.0006533533674 + -0.05112155581x + x2 = 1.0742060253674 Factor a perfect square on the left side: (x + -0.02556077791)(x + -0.02556077791) = 1.0742060253674 Calculate the square root of the right side: 1.036439108 Break this problem into two subproblems by setting (x + -0.02556077791) equal to 1.036439108 and -1.036439108.Subproblem 1
x + -0.02556077791 = 1.036439108 Simplifying x + -0.02556077791 = 1.036439108 Reorder the terms: -0.02556077791 + x = 1.036439108 Solving -0.02556077791 + x = 1.036439108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02556077791' to each side of the equation. -0.02556077791 + 0.02556077791 + x = 1.036439108 + 0.02556077791 Combine like terms: -0.02556077791 + 0.02556077791 = 0.00000000000 0.00000000000 + x = 1.036439108 + 0.02556077791 x = 1.036439108 + 0.02556077791 Combine like terms: 1.036439108 + 0.02556077791 = 1.06199988591 x = 1.06199988591 Simplifying x = 1.06199988591Subproblem 2
x + -0.02556077791 = -1.036439108 Simplifying x + -0.02556077791 = -1.036439108 Reorder the terms: -0.02556077791 + x = -1.036439108 Solving -0.02556077791 + x = -1.036439108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02556077791' to each side of the equation. -0.02556077791 + 0.02556077791 + x = -1.036439108 + 0.02556077791 Combine like terms: -0.02556077791 + 0.02556077791 = 0.00000000000 0.00000000000 + x = -1.036439108 + 0.02556077791 x = -1.036439108 + 0.02556077791 Combine like terms: -1.036439108 + 0.02556077791 = -1.01087833009 x = -1.01087833009 Simplifying x = -1.01087833009Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.06199988591, -1.01087833009}
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