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Simplifying -0.03x2 + 0.03x + 9.5 = 0 Reorder the terms: 9.5 + 0.03x + -0.03x2 = 0 Solving 9.5 + 0.03x + -0.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. -316.6666667 + -1x + x2 = 0 Move the constant term to the right: Add '316.6666667' to each side of the equation. -316.6666667 + -1x + 316.6666667 + x2 = 0 + 316.6666667 Reorder the terms: -316.6666667 + 316.6666667 + -1x + x2 = 0 + 316.6666667 Combine like terms: -316.6666667 + 316.6666667 = 0.0000000 0.0000000 + -1x + x2 = 0 + 316.6666667 -1x + x2 = 0 + 316.6666667 Combine like terms: 0 + 316.6666667 = 316.6666667 -1x + x2 = 316.6666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 316.6666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 316.6666667 + 0.25 Combine like terms: 316.6666667 + 0.25 = 316.9166667 0.25 + -1x + x2 = 316.9166667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 316.9166667 Calculate the square root of the right side: 17.802153429 Break this problem into two subproblems by setting (x + -0.5) equal to 17.802153429 and -17.802153429.Subproblem 1
x + -0.5 = 17.802153429 Simplifying x + -0.5 = 17.802153429 Reorder the terms: -0.5 + x = 17.802153429 Solving -0.5 + x = 17.802153429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 17.802153429 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 17.802153429 + 0.5 x = 17.802153429 + 0.5 Combine like terms: 17.802153429 + 0.5 = 18.302153429 x = 18.302153429 Simplifying x = 18.302153429Subproblem 2
x + -0.5 = -17.802153429 Simplifying x + -0.5 = -17.802153429 Reorder the terms: -0.5 + x = -17.802153429 Solving -0.5 + x = -17.802153429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -17.802153429 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -17.802153429 + 0.5 x = -17.802153429 + 0.5 Combine like terms: -17.802153429 + 0.5 = -17.302153429 x = -17.302153429 Simplifying x = -17.302153429Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.302153429, -17.302153429}
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