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Simplifying 1.5 = -0.00004x2 + 0.0139x + 1.0188 Reorder the terms: 1.5 = 1.0188 + 0.0139x + -0.00004x2 Solving 1.5 = 1.0188 + 0.0139x + -0.00004x2 Solving for variable 'x'. Combine like terms: 1.5 + -1.0188 = 0.4812 0.4812 + -0.0139x + 0.00004x2 = 1.0188 + 0.0139x + -0.00004x2 + -1.0188 + -0.0139x + 0.00004x2 Reorder the terms: 0.4812 + -0.0139x + 0.00004x2 = 1.0188 + -1.0188 + 0.0139x + -0.0139x + -0.00004x2 + 0.00004x2 Combine like terms: 1.0188 + -1.0188 = 0.0000 0.4812 + -0.0139x + 0.00004x2 = 0.0000 + 0.0139x + -0.0139x + -0.00004x2 + 0.00004x2 0.4812 + -0.0139x + 0.00004x2 = 0.0139x + -0.0139x + -0.00004x2 + 0.00004x2 Combine like terms: 0.0139x + -0.0139x = 0.0000 0.4812 + -0.0139x + 0.00004x2 = 0.0000 + -0.00004x2 + 0.00004x2 0.4812 + -0.0139x + 0.00004x2 = -0.00004x2 + 0.00004x2 Combine like terms: -0.00004x2 + 0.00004x2 = 0.00000 0.4812 + -0.0139x + 0.00004x2 = 0.00000 Begin completing the square. Divide all terms by 0.00004 the coefficient of the squared term: Divide each side by '0.00004'. 12030 + -347.5x + x2 = 0 Move the constant term to the right: Add '-12030' to each side of the equation. 12030 + -347.5x + -12030 + x2 = 0 + -12030 Reorder the terms: 12030 + -12030 + -347.5x + x2 = 0 + -12030 Combine like terms: 12030 + -12030 = 0 0 + -347.5x + x2 = 0 + -12030 -347.5x + x2 = 0 + -12030 Combine like terms: 0 + -12030 = -12030 -347.5x + x2 = -12030 The x term is -347.5x. Take half its coefficient (-173.75). Square it (30189.0625) and add it to both sides. Add '30189.0625' to each side of the equation. -347.5x + 30189.0625 + x2 = -12030 + 30189.0625 Reorder the terms: 30189.0625 + -347.5x + x2 = -12030 + 30189.0625 Combine like terms: -12030 + 30189.0625 = 18159.0625 30189.0625 + -347.5x + x2 = 18159.0625 Factor a perfect square on the left side: (x + -173.75)(x + -173.75) = 18159.0625 Calculate the square root of the right side: 134.755565748 Break this problem into two subproblems by setting (x + -173.75) equal to 134.755565748 and -134.755565748.Subproblem 1
x + -173.75 = 134.755565748 Simplifying x + -173.75 = 134.755565748 Reorder the terms: -173.75 + x = 134.755565748 Solving -173.75 + x = 134.755565748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '173.75' to each side of the equation. -173.75 + 173.75 + x = 134.755565748 + 173.75 Combine like terms: -173.75 + 173.75 = 0.00 0.00 + x = 134.755565748 + 173.75 x = 134.755565748 + 173.75 Combine like terms: 134.755565748 + 173.75 = 308.505565748 x = 308.505565748 Simplifying x = 308.505565748Subproblem 2
x + -173.75 = -134.755565748 Simplifying x + -173.75 = -134.755565748 Reorder the terms: -173.75 + x = -134.755565748 Solving -173.75 + x = -134.755565748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '173.75' to each side of the equation. -173.75 + 173.75 + x = -134.755565748 + 173.75 Combine like terms: -173.75 + 173.75 = 0.00 0.00 + x = -134.755565748 + 173.75 x = -134.755565748 + 173.75 Combine like terms: -134.755565748 + 173.75 = 38.994434252 x = 38.994434252 Simplifying x = 38.994434252Solution
The solution to the problem is based on the solutions from the subproblems. x = {308.505565748, 38.994434252}
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