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Simplifying 0.005x2 + -0.01x + -9.68 = 0 Reorder the terms: -9.68 + -0.01x + 0.005x2 = 0 Solving -9.68 + -0.01x + 0.005x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.005 the coefficient of the squared term: Divide each side by '0.005'. -1936 + -2x + x2 = 0 Move the constant term to the right: Add '1936' to each side of the equation. -1936 + -2x + 1936 + x2 = 0 + 1936 Reorder the terms: -1936 + 1936 + -2x + x2 = 0 + 1936 Combine like terms: -1936 + 1936 = 0 0 + -2x + x2 = 0 + 1936 -2x + x2 = 0 + 1936 Combine like terms: 0 + 1936 = 1936 -2x + x2 = 1936 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1936 + 1 Reorder the terms: 1 + -2x + x2 = 1936 + 1 Combine like terms: 1936 + 1 = 1937 1 + -2x + x2 = 1937 Factor a perfect square on the left side: (x + -1)(x + -1) = 1937 Calculate the square root of the right side: 44.011362169 Break this problem into two subproblems by setting (x + -1) equal to 44.011362169 and -44.011362169.Subproblem 1
x + -1 = 44.011362169 Simplifying x + -1 = 44.011362169 Reorder the terms: -1 + x = 44.011362169 Solving -1 + x = 44.011362169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 44.011362169 + 1 Combine like terms: -1 + 1 = 0 0 + x = 44.011362169 + 1 x = 44.011362169 + 1 Combine like terms: 44.011362169 + 1 = 45.011362169 x = 45.011362169 Simplifying x = 45.011362169Subproblem 2
x + -1 = -44.011362169 Simplifying x + -1 = -44.011362169 Reorder the terms: -1 + x = -44.011362169 Solving -1 + x = -44.011362169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -44.011362169 + 1 Combine like terms: -1 + 1 = 0 0 + x = -44.011362169 + 1 x = -44.011362169 + 1 Combine like terms: -44.011362169 + 1 = -43.011362169 x = -43.011362169 Simplifying x = -43.011362169Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.011362169, -43.011362169}
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