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Simplifying 1885.674x2 + -153712.84x + 16950 = 0 Reorder the terms: 16950 + -153712.84x + 1885.674x2 = 0 Solving 16950 + -153712.84x + 1885.674x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1885.674 the coefficient of the squared term: Divide each side by '1885.674'. 8.988828398 + -81.51612633x + x2 = 0 Move the constant term to the right: Add '-8.988828398' to each side of the equation. 8.988828398 + -81.51612633x + -8.988828398 + x2 = 0 + -8.988828398 Reorder the terms: 8.988828398 + -8.988828398 + -81.51612633x + x2 = 0 + -8.988828398 Combine like terms: 8.988828398 + -8.988828398 = 0.000000000 0.000000000 + -81.51612633x + x2 = 0 + -8.988828398 -81.51612633x + x2 = 0 + -8.988828398 Combine like terms: 0 + -8.988828398 = -8.988828398 -81.51612633x + x2 = -8.988828398 The x term is -81.51612633x. Take half its coefficient (-40.75806317). Square it (1661.219713) and add it to both sides. Add '1661.219713' to each side of the equation. -81.51612633x + 1661.219713 + x2 = -8.988828398 + 1661.219713 Reorder the terms: 1661.219713 + -81.51612633x + x2 = -8.988828398 + 1661.219713 Combine like terms: -8.988828398 + 1661.219713 = 1652.230884602 1661.219713 + -81.51612633x + x2 = 1652.230884602 Factor a perfect square on the left side: (x + -40.75806317)(x + -40.75806317) = 1652.230884602 Calculate the square root of the right side: 40.647643039 Break this problem into two subproblems by setting (x + -40.75806317) equal to 40.647643039 and -40.647643039.Subproblem 1
x + -40.75806317 = 40.647643039 Simplifying x + -40.75806317 = 40.647643039 Reorder the terms: -40.75806317 + x = 40.647643039 Solving -40.75806317 + x = 40.647643039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.75806317' to each side of the equation. -40.75806317 + 40.75806317 + x = 40.647643039 + 40.75806317 Combine like terms: -40.75806317 + 40.75806317 = 0.00000000 0.00000000 + x = 40.647643039 + 40.75806317 x = 40.647643039 + 40.75806317 Combine like terms: 40.647643039 + 40.75806317 = 81.405706209 x = 81.405706209 Simplifying x = 81.405706209Subproblem 2
x + -40.75806317 = -40.647643039 Simplifying x + -40.75806317 = -40.647643039 Reorder the terms: -40.75806317 + x = -40.647643039 Solving -40.75806317 + x = -40.647643039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.75806317' to each side of the equation. -40.75806317 + 40.75806317 + x = -40.647643039 + 40.75806317 Combine like terms: -40.75806317 + 40.75806317 = 0.00000000 0.00000000 + x = -40.647643039 + 40.75806317 x = -40.647643039 + 40.75806317 Combine like terms: -40.647643039 + 40.75806317 = 0.110420131 x = 0.110420131 Simplifying x = 0.110420131Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.405706209, 0.110420131}
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