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Simplifying 20 = 0.0178x2 + 1.5x + 16 Reorder the terms: 20 = 16 + 1.5x + 0.0178x2 Solving 20 = 16 + 1.5x + 0.0178x2 Solving for variable 'x'. Combine like terms: 20 + -16 = 4 4 + -1.5x + -0.0178x2 = 16 + 1.5x + 0.0178x2 + -16 + -1.5x + -0.0178x2 Reorder the terms: 4 + -1.5x + -0.0178x2 = 16 + -16 + 1.5x + -1.5x + 0.0178x2 + -0.0178x2 Combine like terms: 16 + -16 = 0 4 + -1.5x + -0.0178x2 = 0 + 1.5x + -1.5x + 0.0178x2 + -0.0178x2 4 + -1.5x + -0.0178x2 = 1.5x + -1.5x + 0.0178x2 + -0.0178x2 Combine like terms: 1.5x + -1.5x = 0.0 4 + -1.5x + -0.0178x2 = 0.0 + 0.0178x2 + -0.0178x2 4 + -1.5x + -0.0178x2 = 0.0178x2 + -0.0178x2 Combine like terms: 0.0178x2 + -0.0178x2 = 0.0000 4 + -1.5x + -0.0178x2 = 0.0000 Begin completing the square. Divide all terms by -0.0178 the coefficient of the squared term: Divide each side by '-0.0178'. -224.7191011 + 84.26966292x + x2 = 0 Move the constant term to the right: Add '224.7191011' to each side of the equation. -224.7191011 + 84.26966292x + 224.7191011 + x2 = 0 + 224.7191011 Reorder the terms: -224.7191011 + 224.7191011 + 84.26966292x + x2 = 0 + 224.7191011 Combine like terms: -224.7191011 + 224.7191011 = 0.0000000 0.0000000 + 84.26966292x + x2 = 0 + 224.7191011 84.26966292x + x2 = 0 + 224.7191011 Combine like terms: 0 + 224.7191011 = 224.7191011 84.26966292x + x2 = 224.7191011 The x term is 84.26966292x. Take half its coefficient (42.13483146). Square it (1775.344022) and add it to both sides. Add '1775.344022' to each side of the equation. 84.26966292x + 1775.344022 + x2 = 224.7191011 + 1775.344022 Reorder the terms: 1775.344022 + 84.26966292x + x2 = 224.7191011 + 1775.344022 Combine like terms: 224.7191011 + 1775.344022 = 2000.0631231 1775.344022 + 84.26966292x + x2 = 2000.0631231 Factor a perfect square on the left side: (x + 42.13483146)(x + 42.13483146) = 2000.0631231 Calculate the square root of the right side: 44.722065282 Break this problem into two subproblems by setting (x + 42.13483146) equal to 44.722065282 and -44.722065282.Subproblem 1
x + 42.13483146 = 44.722065282 Simplifying x + 42.13483146 = 44.722065282 Reorder the terms: 42.13483146 + x = 44.722065282 Solving 42.13483146 + x = 44.722065282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.13483146' to each side of the equation. 42.13483146 + -42.13483146 + x = 44.722065282 + -42.13483146 Combine like terms: 42.13483146 + -42.13483146 = 0.00000000 0.00000000 + x = 44.722065282 + -42.13483146 x = 44.722065282 + -42.13483146 Combine like terms: 44.722065282 + -42.13483146 = 2.587233822 x = 2.587233822 Simplifying x = 2.587233822Subproblem 2
x + 42.13483146 = -44.722065282 Simplifying x + 42.13483146 = -44.722065282 Reorder the terms: 42.13483146 + x = -44.722065282 Solving 42.13483146 + x = -44.722065282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.13483146' to each side of the equation. 42.13483146 + -42.13483146 + x = -44.722065282 + -42.13483146 Combine like terms: 42.13483146 + -42.13483146 = 0.00000000 0.00000000 + x = -44.722065282 + -42.13483146 x = -44.722065282 + -42.13483146 Combine like terms: -44.722065282 + -42.13483146 = -86.856896742 x = -86.856896742 Simplifying x = -86.856896742Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.587233822, -86.856896742}
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