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Simplifying 100x2 + -6x + -124 = 0 Reorder the terms: -124 + -6x + 100x2 = 0 Solving -124 + -6x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-62 + -3x + 50x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-62 + -3x + 50x2)' equal to zero and attempt to solve: Simplifying -62 + -3x + 50x2 = 0 Solving -62 + -3x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -1.24 + -0.06x + x2 = 0.0 Move the constant term to the right: Add '1.24' to each side of the equation. -1.24 + -0.06x + 1.24 + x2 = 0.0 + 1.24 Reorder the terms: -1.24 + 1.24 + -0.06x + x2 = 0.0 + 1.24 Combine like terms: -1.24 + 1.24 = 0.00 0.00 + -0.06x + x2 = 0.0 + 1.24 -0.06x + x2 = 0.0 + 1.24 Combine like terms: 0.0 + 1.24 = 1.24 -0.06x + x2 = 1.24 The x term is -0.06x. Take half its coefficient (-0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. -0.06x + 0.0009 + x2 = 1.24 + 0.0009 Reorder the terms: 0.0009 + -0.06x + x2 = 1.24 + 0.0009 Combine like terms: 1.24 + 0.0009 = 1.2409 0.0009 + -0.06x + x2 = 1.2409 Factor a perfect square on the left side: (x + -0.03)(x + -0.03) = 1.2409 Calculate the square root of the right side: 1.113956911 Break this problem into two subproblems by setting (x + -0.03) equal to 1.113956911 and -1.113956911.Subproblem 1
x + -0.03 = 1.113956911 Simplifying x + -0.03 = 1.113956911 Reorder the terms: -0.03 + x = 1.113956911 Solving -0.03 + x = 1.113956911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = 1.113956911 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = 1.113956911 + 0.03 x = 1.113956911 + 0.03 Combine like terms: 1.113956911 + 0.03 = 1.143956911 x = 1.143956911 Simplifying x = 1.143956911Subproblem 2
x + -0.03 = -1.113956911 Simplifying x + -0.03 = -1.113956911 Reorder the terms: -0.03 + x = -1.113956911 Solving -0.03 + x = -1.113956911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = -1.113956911 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = -1.113956911 + 0.03 x = -1.113956911 + 0.03 Combine like terms: -1.113956911 + 0.03 = -1.083956911 x = -1.083956911 Simplifying x = -1.083956911Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.143956911, -1.083956911}Solution
x = {1.143956911, -1.083956911}
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