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Simplifying 120x2 + -20x + -50 = 0 Reorder the terms: -50 + -20x + 120x2 = 0 Solving -50 + -20x + 120x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-5 + -2x + 12x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-5 + -2x + 12x2)' equal to zero and attempt to solve: Simplifying -5 + -2x + 12x2 = 0 Solving -5 + -2x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.1666666667x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.1666666667x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.1666666667x + x2 = 0 + 0.4166666667 -0.1666666667x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.1666666667x + x2 = 0.4166666667 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 0.4166666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 0.4166666667 + 0.006944444447 Combine like terms: 0.4166666667 + 0.006944444447 = 0.423611111147 0.006944444447 + -0.1666666667x + x2 = 0.423611111147 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 0.423611111147 Calculate the square root of the right side: 0.65085414 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 0.65085414 and -0.65085414.Subproblem 1
x + -0.08333333335 = 0.65085414 Simplifying x + -0.08333333335 = 0.65085414 Reorder the terms: -0.08333333335 + x = 0.65085414 Solving -0.08333333335 + x = 0.65085414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 0.65085414 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.65085414 + 0.08333333335 x = 0.65085414 + 0.08333333335 Combine like terms: 0.65085414 + 0.08333333335 = 0.73418747335 x = 0.73418747335 Simplifying x = 0.73418747335Subproblem 2
x + -0.08333333335 = -0.65085414 Simplifying x + -0.08333333335 = -0.65085414 Reorder the terms: -0.08333333335 + x = -0.65085414 Solving -0.08333333335 + x = -0.65085414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -0.65085414 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.65085414 + 0.08333333335 x = -0.65085414 + 0.08333333335 Combine like terms: -0.65085414 + 0.08333333335 = -0.56752080665 x = -0.56752080665 Simplifying x = -0.56752080665Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73418747335, -0.56752080665}Solution
x = {0.73418747335, -0.56752080665}
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