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Simplifying 100 = 6x + -0.03x2 Solving 100 = 6x + -0.03x2 Solving for variable 'x'. Reorder the terms: 100 + -6x + 0.03x2 = 6x + -6x + -0.03x2 + 0.03x2 Combine like terms: 6x + -6x = 0 100 + -6x + 0.03x2 = 0 + -0.03x2 + 0.03x2 100 + -6x + 0.03x2 = -0.03x2 + 0.03x2 Combine like terms: -0.03x2 + 0.03x2 = 0.00 100 + -6x + 0.03x2 = 0.00 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 3333.333333 + -200x + x2 = 0 Move the constant term to the right: Add '-3333.333333' to each side of the equation. 3333.333333 + -200x + -3333.333333 + x2 = 0 + -3333.333333 Reorder the terms: 3333.333333 + -3333.333333 + -200x + x2 = 0 + -3333.333333 Combine like terms: 3333.333333 + -3333.333333 = 0.000000 0.000000 + -200x + x2 = 0 + -3333.333333 -200x + x2 = 0 + -3333.333333 Combine like terms: 0 + -3333.333333 = -3333.333333 -200x + x2 = -3333.333333 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -3333.333333 + 10000 Reorder the terms: 10000 + -200x + x2 = -3333.333333 + 10000 Combine like terms: -3333.333333 + 10000 = 6666.666667 10000 + -200x + x2 = 6666.666667 Factor a perfect square on the left side: (x + -100)(x + -100) = 6666.666667 Calculate the square root of the right side: 81.649658095 Break this problem into two subproblems by setting (x + -100) equal to 81.649658095 and -81.649658095.Subproblem 1
x + -100 = 81.649658095 Simplifying x + -100 = 81.649658095 Reorder the terms: -100 + x = 81.649658095 Solving -100 + x = 81.649658095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 81.649658095 + 100 Combine like terms: -100 + 100 = 0 0 + x = 81.649658095 + 100 x = 81.649658095 + 100 Combine like terms: 81.649658095 + 100 = 181.649658095 x = 181.649658095 Simplifying x = 181.649658095Subproblem 2
x + -100 = -81.649658095 Simplifying x + -100 = -81.649658095 Reorder the terms: -100 + x = -81.649658095 Solving -100 + x = -81.649658095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -81.649658095 + 100 Combine like terms: -100 + 100 = 0 0 + x = -81.649658095 + 100 x = -81.649658095 + 100 Combine like terms: -81.649658095 + 100 = 18.350341905 x = 18.350341905 Simplifying x = 18.350341905Solution
The solution to the problem is based on the solutions from the subproblems. x = {181.649658095, 18.350341905}
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