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Simplifying 0 = -0.007x2 + x + 15 Reorder the terms: 0 = 15 + x + -0.007x2 Solving 0 = 15 + x + -0.007x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -1x + 0.007x2 = 15 + x + -0.007x2 + -15 + -1x + 0.007x2 Reorder the terms: -15 + -1x + 0.007x2 = 15 + -15 + x + -1x + -0.007x2 + 0.007x2 Combine like terms: 15 + -15 = 0 -15 + -1x + 0.007x2 = 0 + x + -1x + -0.007x2 + 0.007x2 -15 + -1x + 0.007x2 = x + -1x + -0.007x2 + 0.007x2 Combine like terms: x + -1x = 0 -15 + -1x + 0.007x2 = 0 + -0.007x2 + 0.007x2 -15 + -1x + 0.007x2 = -0.007x2 + 0.007x2 Combine like terms: -0.007x2 + 0.007x2 = 0.000 -15 + -1x + 0.007x2 = 0.000 Begin completing the square. Divide all terms by 0.007 the coefficient of the squared term: Divide each side by '0.007'. -2142.857143 + -142.8571429x + x2 = 0 Move the constant term to the right: Add '2142.857143' to each side of the equation. -2142.857143 + -142.8571429x + 2142.857143 + x2 = 0 + 2142.857143 Reorder the terms: -2142.857143 + 2142.857143 + -142.8571429x + x2 = 0 + 2142.857143 Combine like terms: -2142.857143 + 2142.857143 = 0.000000 0.000000 + -142.8571429x + x2 = 0 + 2142.857143 -142.8571429x + x2 = 0 + 2142.857143 Combine like terms: 0 + 2142.857143 = 2142.857143 -142.8571429x + x2 = 2142.857143 The x term is -142.8571429x. Take half its coefficient (-71.42857145). Square it (5102.040819) and add it to both sides. Add '5102.040819' to each side of the equation. -142.8571429x + 5102.040819 + x2 = 2142.857143 + 5102.040819 Reorder the terms: 5102.040819 + -142.8571429x + x2 = 2142.857143 + 5102.040819 Combine like terms: 2142.857143 + 5102.040819 = 7244.897962 5102.040819 + -142.8571429x + x2 = 7244.897962 Factor a perfect square on the left side: (x + -71.42857145)(x + -71.42857145) = 7244.897962 Calculate the square root of the right side: 85.116966358 Break this problem into two subproblems by setting (x + -71.42857145) equal to 85.116966358 and -85.116966358.Subproblem 1
x + -71.42857145 = 85.116966358 Simplifying x + -71.42857145 = 85.116966358 Reorder the terms: -71.42857145 + x = 85.116966358 Solving -71.42857145 + x = 85.116966358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.42857145' to each side of the equation. -71.42857145 + 71.42857145 + x = 85.116966358 + 71.42857145 Combine like terms: -71.42857145 + 71.42857145 = 0.00000000 0.00000000 + x = 85.116966358 + 71.42857145 x = 85.116966358 + 71.42857145 Combine like terms: 85.116966358 + 71.42857145 = 156.545537808 x = 156.545537808 Simplifying x = 156.545537808Subproblem 2
x + -71.42857145 = -85.116966358 Simplifying x + -71.42857145 = -85.116966358 Reorder the terms: -71.42857145 + x = -85.116966358 Solving -71.42857145 + x = -85.116966358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.42857145' to each side of the equation. -71.42857145 + 71.42857145 + x = -85.116966358 + 71.42857145 Combine like terms: -71.42857145 + 71.42857145 = 0.00000000 0.00000000 + x = -85.116966358 + 71.42857145 x = -85.116966358 + 71.42857145 Combine like terms: -85.116966358 + 71.42857145 = -13.688394908 x = -13.688394908 Simplifying x = -13.688394908Solution
The solution to the problem is based on the solutions from the subproblems. x = {156.545537808, -13.688394908}
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