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Simplifying 84.487 = -0.012x2 + 1.242x + 64.447 Reorder the terms: 84.487 = 64.447 + 1.242x + -0.012x2 Solving 84.487 = 64.447 + 1.242x + -0.012x2 Solving for variable 'x'. Combine like terms: 84.487 + -64.447 = 20.04 20.04 + -1.242x + 0.012x2 = 64.447 + 1.242x + -0.012x2 + -64.447 + -1.242x + 0.012x2 Reorder the terms: 20.04 + -1.242x + 0.012x2 = 64.447 + -64.447 + 1.242x + -1.242x + -0.012x2 + 0.012x2 Combine like terms: 64.447 + -64.447 = 0.000 20.04 + -1.242x + 0.012x2 = 0.000 + 1.242x + -1.242x + -0.012x2 + 0.012x2 20.04 + -1.242x + 0.012x2 = 1.242x + -1.242x + -0.012x2 + 0.012x2 Combine like terms: 1.242x + -1.242x = 0.000 20.04 + -1.242x + 0.012x2 = 0.000 + -0.012x2 + 0.012x2 20.04 + -1.242x + 0.012x2 = -0.012x2 + 0.012x2 Combine like terms: -0.012x2 + 0.012x2 = 0.000 20.04 + -1.242x + 0.012x2 = 0.000 Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. 1670 + -103.5x + x2 = 0 Move the constant term to the right: Add '-1670' to each side of the equation. 1670 + -103.5x + -1670 + x2 = 0 + -1670 Reorder the terms: 1670 + -1670 + -103.5x + x2 = 0 + -1670 Combine like terms: 1670 + -1670 = 0 0 + -103.5x + x2 = 0 + -1670 -103.5x + x2 = 0 + -1670 Combine like terms: 0 + -1670 = -1670 -103.5x + x2 = -1670 The x term is -103.5x. Take half its coefficient (-51.75). Square it (2678.0625) and add it to both sides. Add '2678.0625' to each side of the equation. -103.5x + 2678.0625 + x2 = -1670 + 2678.0625 Reorder the terms: 2678.0625 + -103.5x + x2 = -1670 + 2678.0625 Combine like terms: -1670 + 2678.0625 = 1008.0625 2678.0625 + -103.5x + x2 = 1008.0625 Factor a perfect square on the left side: (x + -51.75)(x + -51.75) = 1008.0625 Calculate the square root of the right side: 31.75 Break this problem into two subproblems by setting (x + -51.75) equal to 31.75 and -31.75.Subproblem 1
x + -51.75 = 31.75 Simplifying x + -51.75 = 31.75 Reorder the terms: -51.75 + x = 31.75 Solving -51.75 + x = 31.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51.75' to each side of the equation. -51.75 + 51.75 + x = 31.75 + 51.75 Combine like terms: -51.75 + 51.75 = 0.00 0.00 + x = 31.75 + 51.75 x = 31.75 + 51.75 Combine like terms: 31.75 + 51.75 = 83.5 x = 83.5 Simplifying x = 83.5Subproblem 2
x + -51.75 = -31.75 Simplifying x + -51.75 = -31.75 Reorder the terms: -51.75 + x = -31.75 Solving -51.75 + x = -31.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51.75' to each side of the equation. -51.75 + 51.75 + x = -31.75 + 51.75 Combine like terms: -51.75 + 51.75 = 0.00 0.00 + x = -31.75 + 51.75 x = -31.75 + 51.75 Combine like terms: -31.75 + 51.75 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.5, 20}
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