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Simplifying -0.01x2 + -0.3x + 17 = 0 Reorder the terms: 17 + -0.3x + -0.01x2 = 0 Solving 17 + -0.3x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -1700 + 30x + x2 = 0 Move the constant term to the right: Add '1700' to each side of the equation. -1700 + 30x + 1700 + x2 = 0 + 1700 Reorder the terms: -1700 + 1700 + 30x + x2 = 0 + 1700 Combine like terms: -1700 + 1700 = 0 0 + 30x + x2 = 0 + 1700 30x + x2 = 0 + 1700 Combine like terms: 0 + 1700 = 1700 30x + x2 = 1700 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 1700 + 225 Reorder the terms: 225 + 30x + x2 = 1700 + 225 Combine like terms: 1700 + 225 = 1925 225 + 30x + x2 = 1925 Factor a perfect square on the left side: (x + 15)(x + 15) = 1925 Calculate the square root of the right side: 43.874821937 Break this problem into two subproblems by setting (x + 15) equal to 43.874821937 and -43.874821937.Subproblem 1
x + 15 = 43.874821937 Simplifying x + 15 = 43.874821937 Reorder the terms: 15 + x = 43.874821937 Solving 15 + x = 43.874821937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 43.874821937 + -15 Combine like terms: 15 + -15 = 0 0 + x = 43.874821937 + -15 x = 43.874821937 + -15 Combine like terms: 43.874821937 + -15 = 28.874821937 x = 28.874821937 Simplifying x = 28.874821937Subproblem 2
x + 15 = -43.874821937 Simplifying x + 15 = -43.874821937 Reorder the terms: 15 + x = -43.874821937 Solving 15 + x = -43.874821937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -43.874821937 + -15 Combine like terms: 15 + -15 = 0 0 + x = -43.874821937 + -15 x = -43.874821937 + -15 Combine like terms: -43.874821937 + -15 = -58.874821937 x = -58.874821937 Simplifying x = -58.874821937Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.874821937, -58.874821937}
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